@article{MalikZouMarwanetal.2012,
  author    = {Malik, Nishant and Zou, Y. and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Dynamical regimes and transitions in plio-pleistocene Asian monsoon},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {97},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  number    = {4},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/97/40009},
  pages     = {6},
  year      = {2012},
  abstract  = {We propose a novel approach based on the fluctuation of similarity to identify regimes of distinct dynamical complexity in short time series. A statistical test is developed to estimate the significance of the identified transitions. Our method is verified by uncovering bifurcation structures in several paradigmatic models, providing more complex transitions compared with traditional Lyapunov exponents. In a real-world situation, we apply this method to identify millennial-scale dynamical transitions in Plio-Pleistocene proxy records of the South Asian summer monsoon system. We infer that many of these transitions are induced by the external forcing of the solar insolation and are also affected by internal forcing on Monsoonal dynamics, i.e., the glaciation cycles of the Northern Hemisphere and the onset of the Walker circulation.},
  language  = {en}
}
@article{ZhouKurths2006,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Dynamical weights and enhanced synchronization in adaptive complex networks},
  doi       = {10.1103/Physrevlett.96.164102},
  year      = {2006},
  abstract  = {Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks},
  language  = {en}
}
@article{RuzickScheffczykPikovskijetal.1997,
  author    = {Ruzick, Oliver and Scheffczyk, Christian and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Dynamics of chaos-order interface in coupled map lattices},
  year      = {1997},
  language  = {en}
}
@misc{MotterMatiasKurthsetal.2006,
  author    = {Motter, Adilson E. and Matias, Manuel A. and Kurths, J{\"u}rgen and Ott, Edward},
  title     = {Dynamics on complex networks and applications},
  series = {Physica. D, Nonlinear phenomena},
  volume    = {224},
  journal   = {Physica. D, Nonlinear phenomena},
  number    = {1-2},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2006.09.012},
  pages     = {VII -- VIII},
  year      = {2006},
  language  = {en}
}
@article{AnishchenkoVadivasovaKopeikinetal.2001,
  author    = {Anishchenko, Vadim S. and Vadivasova, T. E. and Kopeikin, A. S. and Kurths, J{\"u}rgen and Strelkova, G. I.},
  title     = {Effect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors},
  year      = {2001},
  language  = {en}
}
@article{RosenblumPikovskijKurths1997,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Effect of phase synchronization in driven chaotic oscillators},
  year      = {1997},
  language  = {en}
}
@article{ChenShangZhouetal.2009,
  author    = {Chen, Maoyin and Shang, Yun and Zhou, Changsong and Wu, Ye and Kurths, J{\"u}rgen},
  title     = {Enhanced synchronizability in scale-free networks},
  issn      = {1054-1500},
  doi       = {10.1063/1.3062864},
  year      = {2009},
  abstract  = {We introduce a modified dynamical optimization coupling scheme to enhance the synchronizability in the scale- free networks as well as to keep uniform and converging intensities during the transition to synchronization. Further, the size of networks that can be synchronizable exceeds by several orders of magnitude the size of unweighted networks.},
  language  = {en}
}
@article{MotterZhouKurths2005,
  author    = {Motter, Adilson E. and Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Enhancing complex-network synchronization},
  issn      = {0295-5075},
  year      = {2005},
  abstract  = {Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for enhanced synchronization in weighted networks with asymmetric coupling. We show that, in the optimum regime, synchronizability is solely determined by the average degree and does not depend on the system size and the details of the degree distribution. In scale-free networks, where the average degree may increase with heterogeneity, synchronizability is drastically enhanced and may become positively correlated with heterogeneity, while the overall cost involved in the network coupling is significantly reduced as compared to the case of unwcighted coupling},
  language  = {en}
}
@article{MarwanSchwarzKurthsetal.2000,
  author    = {Marwan, Norbert and Schwarz, Udo and Kurths, J{\"u}rgen and Strecker, Manfred},
  title     = {ENSO Impact on landslide generation in northwestern Argentina},
  issn      = {1029-7006},
  year      = {2000},
  abstract  = {Climatic changes are of major importance in landslide generation in the Argentine Andes. Increased humidity as a potential influential factor was inferred from the temporal clustering of landslide deposits during a period of significantly wetter climate, 30,000 years ago. A change in seasonality was tested by comparing past (inferred from annual-layered lake deposits, 30,000 years old) and modern (present-day observations) precipitation changes. Quantitative analysis of cross recurrence plots were developed to compare the influence of the El Nino/Southern Oscillation (ENSO) on present and past rainfall variations. This analysis has shown the stronger influence of NE trades in the location of landslide deposits in the intra-andean basin and valleys, what caused a higher contrast between summer and winter rainfall and an increasing of precipitation in La Nina years. This is believed to reduce thresholds for landslide generation in the arid to semiarid intra-andean basins and valleys.},
  language  = {en}
}
@article{WesselSchumannWesseletal.2000,
  author    = {Wessel, Niels and Schumann, Agnes and Wessel, Niels and Schumann, Agnes and Schirdewan, Alexander and Voss, Andreas and Kurths, J{\"u}rgen},
  title     = {Entropy measures in heart rate variability data},
  year      = {2000},
  language  = {en}
}
@article{MaraunKurths2005,
  author    = {Maraun, Douglas and Kurths, J{\"u}rgen},
  title     = {Epochs of phase coherence between El Nino/Southern Oscillation and Indian monsoon},
  issn      = {0094-8276},
  year      = {2005},
  abstract  = {We present a modern method used in nonlinear time series analysis to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. We study the difference of the phase dynamics between El Nino/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales. We identify distinct epochs, especially two intervals of phase coherence, 1886 - 1908 and 1964 - 1980, corroborating earlier findings from a new point of view. A significance test shows that the coherence is very unlikely to be the result of stochastic fluctuations. We also detect so far unknown periods of coupling which are invisible to linear methods. These findings suggest that the decreasing correlation during the last decades might be a typical epoch of the ENSO/ Monsoon system having occurred repeatedly. The high time resolution of the method enables us to present an interpretation of how volcanic radiative forcing could cause the coupling},
  language  = {en}
}
@article{SchwacheKurthsMitschkeetal.1999,
  author    = {Schwache, A. and Kurths, J{\"u}rgen and Mitschke, F. and Voss, Henning U.},
  title     = {Equations of motion from chaotic data : a driven optical fiber ring resonator},
  year      = {1999},
  language  = {en}
}
@article{ThielRomanoReadetal.2004,
  author    = {Thiel, M. and Romano, Maria Carmen and Read, P. L. and Kurths, J{\"u}rgen},
  title     = {Estimation of dynamical invariants without embedding by recurrence plots},
  issn      = {1054-1500},
  year      = {2004},
  abstract  = {In this paper we show that two dynamical invariants, the second order Renyi entropy and the correlation dimension, can be estimated from recurrence plots (RPs) with arbitrary embedding dimension and delay. This fact is interesting as these quantities are even invariant if no embedding is used. This is an important advantage of RPs compared to other techniques of nonlinear data analysis. These estimates for the correlation dimension and entropy are robust and, moreover, can be obtained at a low numerical cost. We exemplify our results for the Rossler system, the funnel attractor and the Mackey-Glass system. In the last part of the paper we estimate dynamical invariants for data from some fluid dynamical experiments and confirm previous evidence for low dimensional chaos in this experimental system. (C) 2004 American Institute of Physics},
  language  = {en}
}
@article{RaabKurths2001,
  author    = {Raab, Corinna and Kurths, J{\"u}rgen},
  title     = {Estimation of Large-Scale Dimension Densities},
  year      = {2001},
  abstract  = {We propose a technique to calculate large-scale dimension densities in both higher-dimensional spatio-temporal systems and low-dimensional systems from only a few data points, where known methods usually have an unsatisfactory scaling behavior. This is mainly due to boundary and finite size effects. With our rather simple method we normalize boundary effects and get a significant correction of the dimension estimate. This straightforward approach is basing on rather general assumptions. So even weak coherent structures obtained from small spatial couplings can be detected with this method, what is impossible by using the Lyapunov-dimension density. We demonstrate the efficiency of our technique for coupled logistic maps, coupled tent maps, the Lorenz-attractor and the Roessler-attractor.},
  language  = {en}
}
@article{SitzSchwarzKurthsetal.2002,
  author    = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen and Voss, Henning U.},
  title     = {Estimation of parameters and unobserved components for nonlinear systems from noisy time series},
  year      = {2002},
  abstract  = {We study the problem of simultaneous estimation of parameters and unobserved states from noisy data of nonlinear time-continuous systems, including the case of additive stochastic forcing. We propose a solution by adapting the recently developed statistical method of unscented Kalman filtering to this problem. Due to its recursive and derivative-free structure, this method minimizes the cost function in a computationally efficient and robust way. It is found that parameters as well as unobserved components can be estimated with high accuracy, including confidence bands, from heavily noise-corrupted data.},
  language  = {en}
}
@article{WesselVossKurthsetal.2000,
  author    = {Wessel, Niels and Voss, Andreas and Kurths, J{\"u}rgen and Schirdewan, Alexander and Hnatkova, Katarina and Malik, Marek},
  title     = {Evaluation of renormalised entropy for risk stratification using heart rate variability data},
  year      = {2000},
  abstract  = {Standard time and frequency parameters of heart rate variability (HRV) describe only linear and periodic behaviour, whereas more complex relationships cannot be recognised. A method that may be capable of assessing more complex properties is the non-linear measure of 'renormalised entropy.' A new concept of the method, RE(AR), has been developed, based on a non-linear renormalisation of autoregressive spectral distributions. To test the hypothesis that renormalised entropy may improve the result of high-risk stratification after myocardial infarction, it is applied to a clinical pilot study (41 subjects) and to prospective data of the St George's Hospital post- infarction database (572 patients). The study shows that the new RE(AR) method is more reproducible and more stable in time than a previously introduced method (p<0.001). Moreover, the results of the study confirm the hypothesis that on average, the survivors have negative values of RE(AR) (-0.11+/-0.18), whereas the non-survivors have positive values (0.03+/-0.22, p<0.01). Further, the study shows that the combination of an HRV triangular index and RE(AR) leads to a better prediction of sudden arrhythmic death than standard measurements of HRV. In summary, the new RE(AR) method is an independent measure in HRV analysis that may be suitable for risk stratification in patients after myocardial infarction.},
  language  = {en}
}
@article{WuZhouXiaoetal.2010,
  author    = {Wu, Ye Wu and Zhou, Changsong and Xiao, Jinghua and Kurths, J{\"u}rgen and Schellnhuber, Hans Joachim},
  title     = {Evidence for a bimodal distribution in human communication},
  issn      = {0027-8424},
  doi       = {10.1073/pnas.1013140107},
  year      = {2010},
  abstract  = {Interacting human activities underlie the patterns of many social, technological, and economic phenomena. Here we present clear empirical evidence from Short Message correspondence that observed human actions are the result of the interplay of three basic ingredients: Poisson initiation of tasks and decision making for task execution in individual humans as well as interaction among individuals. This interplay leads to new types of interevent time distribution, neither completely Poisson nor power-law, but a bimodal combination of them. We show that the events can be separated into independent bursts which are generated by frequent mutual interactions in short times following random initiations of communications in longer times by the individuals. We introduce a minimal model of two interacting priority queues incorporating the three basic ingredients which fits well the distributions using the parameters extracted from the empirical data. The model can also embrace a range of realistic social interacting systems such as e-mail and letter communications when taking the time scale of processing into account. Our findings provide insight into various human activities both at the individual and network level. Our analysis and modeling of bimodal activity in human communication from the viewpoint of the interplay between processes of different time scales is likely to shed light on bimodal phenomena in other complex systems, such as interevent times in earthquakes, rainfall, forest fire, and economic systems, etc.},
  language  = {en}
}
@article{DanaBlasiusKurths2006,
  author    = {Dana, Syamal Kumar and Blasius, Bernd and Kurths, J{\"u}rgen},
  title     = {Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators},
  issn      = {1054-1500},
  doi       = {10.1063/1.2197168},
  year      = {2006},
  abstract  = {We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models},
  language  = {en}
}
@article{SurovyatkinaKravtsovKurths2005,
  author    = {Surovyatkina, E. D. and Kravtsov, Y. A. and Kurths, J{\"u}rgen},
  title     = {Fluctuation growth and saturation in nonlinear oscillators on the threshold of bifurcation of spontaneous symmetry breaking},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We study prebifurcation fluctuation amplification in nonlinear oscillators subject to bifurcations of spontaneous symmetry breaking which are manifest in the doubling of stable equilibrium states. Our theoretical estimates of both the linear growth and the nonlinear saturation of the fluctuations are in good agreement with our results from numerical simulations. We show that in the saturation mode, the fluctuation variance is proportional to the standard deviation of the external noise, whereas in the linear mode, the fluctuation variance is proportional to the noise variance. It is demonstrated that the phenomenon of prebifurcation noise amplification is more pronounced in the case of a slow transition through the bifurcation point. The amplification of fluctuations in this case makes it easier to form a symmetric probability of the final equilibrium states. In contrast, for a fast transition through the bifurcation point, the effect of amplification is much less pronounced. Under backward and forward passages through the bifurcation point, a loop of noise-dependent hysteresis emerges here. We find that for a fast transition of the nonlinear oscillator through the bifurcation point, the probability symmetry of the final equilibrium states is destroyed},
  language  = {en}
}
@article{BoveBoccalettiBragardetal.2004,
  author    = {Bove, I. and Boccaletti, Stefano and Bragard, Jean and Kurths, J{\"u}rgen and Mancini, H.},
  title     = {Frequency entrainment of nonautonomous chaotic oscillators},
  year      = {2004},
  abstract  = {We give evidence of frequency entrainment of dominant peaks in the chaotic spectra of two coupled chaotic nonautonomous oscillators. At variance with the autonomous case, the phenomenon is here characterized by the vanishing of a previously positive Lyapunov exponent in the spectrum, which takes place for a broad range of the coupling strength parameter. Such a state is studied also for the case of chaotic oscillators with ill-defined phases due to the absence of a unique center of rotation. Different phase synchronization indicators are used to circumvent this difficulty},
  language  = {en}
}
@article{VolkovUllnerZaikinetal.2003,
  author    = {Volkov, E. I. and Ullner, Ekkehard and Zaikin, Alexei A. and Kurths, J{\"u}rgen},
  title     = {Frequency-dependent stochastic resonance in inhibitory coupled excitable systems},
  issn      = {1063-651X},
  year      = {2003},
  abstract  = {We study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise- supported stochastic attractors which are created due to slow variable diffusion between identical excitable elements. Such a coupling provides coexisting of several average periods distinct from that of an isolated oscillator and several phase relations between elements. We show that the response of the coupled elements under different noise levels can be significantly enhanced or reduced by forcing some elements in resonance with these new frequencies which correspond to appropriate phase relations},
  language  = {en}
}
@article{RosenblumPikovskijKurths1997,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {From Phase to Lag Synchronization in Coupled Chaotic Oscillators},
  year      = {1997},
  abstract  = {We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe thisregime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.},
  language  = {en}
}
@misc{ThielRomanoKurthsetal.2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold},
  title     = {Generating Surrogates from Recurrences},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56906},
  year      = {2006},
  abstract  = {In this paper we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres.},
  language  = {en}
}
@article{PereiraBaptistaReyesetal.2006,
  author    = {Pereira, Tiago and Baptista, Murilo da Silva and Reyes, Marcelo Bussotti and Caldas, Ibere Luiz and Sartorelli, Jos{\´e} Carlos and Kurths, J{\"u}rgen},
  title     = {Global bifurcation destroying the experimental torus T-2},
  doi       = {10.1103/Physreve.73.017201},
  year      = {2006},
  abstract  = {We show experimentally the scenario of a two-frequency torus T-2 breakdown, in which a global bifurcation occurs due to the collision of a torus with an unstable periodic orbit, creating a heteroclinic saddle connection, followed by an intermittent behavior},
  language  = {en}
}
@article{SureshSenthilkumarLakshmananetal.2010,
  author    = {Suresh, R. and Senthilkumar, Dharmapuri Vijayan and Lakshmanan, Muthusamy and Kurths, J{\"u}rgen},
  title     = {Global phase synchronization in an array of time-delay systems},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.82.016215},
  year      = {2010},
  abstract  = {We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.},
  language  = {en}
}
@article{RosenblumKurthsSchaeferetal.1998,
  author    = {Rosenblum, Michael and Kurths, J{\"u}rgen and Sch{\"a}fer, Carsten and Abel, Hans-Henning},
  title     = {Heartbeat synchronized with ventilation},
  year      = {1998},
  language  = {en}
}
@article{ZhouZemanovaZamoraetal.2006,
  author    = {Zhou, Changsong and Zemanova, Lucia and Zamora, Gorka and Hilgetag, Claus C. and Kurths, J{\"u}rgen},
  title     = {Hierarchical organization unveiled by functional connectivity in complex brain networks},
  series = {Physical review letters},
  volume    = {97},
  journal   = {Physical review letters},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.97.238103},
  pages     = {4},
  year      = {2006},
  abstract  = {How do diverse dynamical patterns arise from the topology of complex networks? We study synchronization dynamics in the cortical brain network of the cat, which displays a hierarchically clustered organization, by modeling each node (cortical area) with a subnetwork of interacting excitable neurons. We find that in the biologically plausible regime the dynamics exhibits a hierarchical modular organization, in particular, revealing functional clusters coinciding with the anatomical communities at different scales. Our results provide insights into the relationship between network topology and functional organization of complex brain networks.},
  language  = {en}
}
@article{ZhouKurths2006,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Hierarchical synchronization in complex networks with heterogeneous degrees},
  issn      = {1054-1500},
  doi       = {10.1063/1.2150381},
  year      = {2006},
  abstract  = {We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function. (C) 2006 American Institute of Physics},
  language  = {en}
}
@article{CiemerBoersHirotaetal.2019,
  author    = {Ciemer, Catrin and Boers, Niklas and Hirota, Marina and Kurths, J{\"u}rgen and M{\"u}ller-Hansen, Finn and Oliveira, Rafael S. and Winkelmann, Ricarda},
  title     = {Higher resilience to climatic disturbances in tropical vegetation exposed to more variable rainfall},
  series = {Nature geoscience},
  volume    = {12},
  journal   = {Nature geoscience},
  number    = {3},
  publisher = {Nature Publ. Group},
  address   = {New York},
  issn      = {1752-0894},
  doi       = {10.1038/s41561-019-0312-z},
  pages     = {174 -- 179},
  year      = {2019},
  abstract  = {With ongoing global warming, the amount and frequency of precipitation in the tropics is projected to change substantially. While it has been shown that tropical forests and savannahs are sustained within the same intermediate mean annual precipitation range, the mechanisms that lead to the resilience of these ecosystems are still not fully understood. In particular, the long-term impact of rainfall variability on resilience is as yet unclear. Here we present observational evidence that both tropical forest and savannah exposed to a higher rainfall variability-in particular on interannual scales-during their long-term past are overall more resilient against climatic disturbances. Based on precipitation and tree cover data in the Brazilian Amazon basin, we constructed potential landscapes that enable us to systematically measure the resilience of the different ecosystems. Additionally, we infer that shifts from forest to savannah due to decreasing precipitation in the future are more likely to occur in regions with a precursory lower rainfall variability. Long-term rainfall variability thus needs to be taken into account in resilience analyses and projections of vegetation response to climate change.},
  language  = {en}
}
@article{GoswamiMarwanFeulneretal.2013,
  author    = {Goswami, Bedartha and Marwan, Norbert and Feulner, Georg and Kurths, J{\"u}rgen},
  title     = {How do global temperature drivers influence each other?},
  series = {European physical journal special topics},
  volume    = {222},
  journal   = {European physical journal special topics},
  number    = {3-4},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2013-01889-8},
  pages     = {861 -- 873},
  year      = {2013},
  abstract  = {We investigate a network of influences connected to global mean temperature. Considering various climatic factors known to influence global mean temperature, we evaluate not only the impacts of these factors on temperature but also the directed dependencies among the factors themselves. Based on an existing recurrence-based connectivity measure, we propose a new and more general measure that quantifies the level of dependence between two time series based on joint recurrences at a chosen time delay. The measures estimated in the analysis are tested for statistical significance using twin surrogates. We find, in accordance with earlier studies, the major drivers for global mean temperature to be greenhouse gases, ENSO, volcanic activity, and solar irradiance. We further uncover a feedback between temperature and ENSO. Our results demonstrate the need to involve multiple, delayed interactions within the drivers of temperature in order to develop a more thorough picture of global temperature variations.},
  language  = {en}
}
@article{ThielRomanoKurths2004,
  author    = {Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen},
  title     = {How much information is contained in a recurrence plot?},
  issn      = {0375-9601},
  year      = {2004},
  abstract  = {Recurrence plots have recently been recognized as a powerful tool for the analysis of data. Not only the visualization of structures of the time series but also the possibility to estimate invariants from them and the possibility to analyze non-stationary data sets are remarkable. However, the question of how much information is encoded in such a two-dimensional and binary representation has not been discussed so far. In this Letter we show that-under some conditions-it is possible to reconstruct an attractor from the recurrence plot, at least topologically. This means that all relevant dynamical information is contained in the plot. (C) 2004 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{WuZhouChenetal.2010,
  author    = {Wu, Ye and Zhou, Changsong and Chen, Maoyin and Xiao, Jinghua and Kurths, J{\"u}rgen},
  title     = {Human comment dynamics in on-line social systems},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2010.08.049},
  year      = {2010},
  abstract  = {Human comment is studied using data from 'tianya' which is one of the most popular on-line social systems in China. We found that the time interval between two consecutive comments on the same topic, called inter-event time, follows a power-law distribution. This result shows that there is no characteristic decay time on a topic. It allows for very long periods without comments that separate bursts of intensive comments. Furthermore, the frequency of a different ID commenting on a topic also follows a power-law distribution. It indicates that there are some "hubs" in the topic who lead the direction of the public opinion. Based on the personal comments habit, a model is introduced to explain these phenomena. The numerical simulations of the model fit well with the empirical results. Our findings are helpful for discovering regular patterns of human behavior in on-line society and the evolution of the public opinion on the virtual as well as real society.},
  language  = {en}
}
@article{LandaZaikinUshakovetal.2000,
  author    = {Landa, Polina S. and Zaikin, Alexei A. and Ushakov, V. G. and Kurths, J{\"u}rgen},
  title     = {Influence of additive noise on transitions in nonlinear systems},
  year      = {2000},
  abstract  = {The effect of additive noise on transitions in nonlinear systems far from equilibrium is studied. It is shown that additive noise in itself can induce a hidden phase transition, which is similar to the transition induced by multiplicative noise in a nonlinear oscillator [P. Landa and A. Zaikin, Phys. Rev. E 54, 3535 (1996)]. Investigation of different nonlinear models that demonstrate phase transitions induced by multiplicative noise shows that the influence of additive noise upon such phase transitions can be crucial: additive noise can either blur such a transition or stabilize noise-induced oscillations.},
  language  = {en}
}
@article{OrgisBrandSchwarzetal.2009,
  author    = {Orgis, Thomas and Brand, Sascha and Schwarz, Udo and Handorf, D{\"o}rthe and Dethloff, Klaus and Kurths, J{\"u}rgen},
  title     = {Influence of interactive stratospheric chemistry on large-scale air mass exchange in a global circulation model},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2009-01105-8},
  year      = {2009},
  abstract  = {A new globally uniform Lagrangian transport scheme for large ensembles of passive tracer particles is presented and applied to wind data from a coupled atmosphere-ocean climate model that includes interactive dynamical feedback with stratospheric chemistry. This feedback from the chemistry is found to enhance large-scale meridional air mass exchange in the northern winter stratosphere as well as intrusion of stratospheric air into the troposphere, where both effects are due to a weakened polar vortex.},
  language  = {en}
}
@article{BaptistaZhouKurths2006,
  author    = {Baptista, Murilo da Silva and Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Information transmission in phase synchronous chaotic arrays},
  issn      = {0256-307X},
  doi       = {10.1088/0256-307X/23/3/010},
  year      = {2006},
  abstract  = {We show many versatile phase synchronous configurations that emerge in an array of coupled chaotic elements due to the presence of a periodic stimulus. Then, we explain the relevance of these configurations to the understanding of how information about such a. stimulus is transmitted from one side to the other in this array. The stimulus actively creates the ways to be transmitted, by making the chaotic elements to phase synchronize},
  language  = {en}
}
@article{RusconiVallerianiDunlopetal.2009,
  author    = {Rusconi, Marco and Valleriani, Angelo and Dunlop, John William Chapman and Kurths, J{\"u}rgen and Weinkamer, Richard},
  title     = {Insights into the control of trabecular bone remodelling obtained by a Markov model},
  issn      = {8756-3282},
  doi       = {10.1016/j.bone.2009.03.467},
  year      = {2009},
  language  = {en}
}
@article{SteuerKurthsFiehnetal.2003,
  author    = {Steuer, Ralf and Kurths, J{\"u}rgen and Fiehn, Oliver and Weckwerth, Wolfram},
  title     = {Interpreting correlations in metabolomic networks},
  issn      = {0300-5127},
  year      = {2003},
  abstract  = {Correlations, as observed between the concentrations of metabolites in a biological sample, may be used to gain additional information about the physiological state of a given tissue. in this mini-review, we discuss the integration of these observed correlations into metabolomic networks and their relationships with the underlying biochemical pathways},
  language  = {en}
}
@book{RosenblumSchaeferAbeletal.1997,
  author    = {Rosenblum, Michael and Sch{\"a}fer, Carsten and Abel, Hans-Henning and Kurths, J{\"u}rgen},
  title     = {Interrelationship of Parasympathetic Innervation of the Sinoatrial Node and the Atrioventricular Node of Human Heart},
  issn      = {1120-1797},
  year      = {1997},
  language  = {en}
}
@article{FeudelWittGellertetal.2005,
  author    = {Feudel, Fred and Witt, Annette and Gellert, Marcus and Kurths, J{\"u}rgen and Grebogi, Celso and Sanjuan, Miguel Angel Fernandez},
  title     = {Intersections of stable and unstable manifolds : the skeleton of Lagrangian chaos},
  year      = {2005},
  abstract  = {We study Hamiltonian chaos generated by the dynamics of passive tracers moving in a two-dimensional fluid flow and describe the complex structure formed in a chaotic layer that separates a vortex region from the shear flow. The stable and unstable manifolds of unstable periodic orbits are computed. It is shown that their intersections in the Poincare map as an invariant set of homoclinic points constitute the backbone of the chaotic layer. Special attention is paid to the finite time properties of the chaotic layer. In particular, finite time Lyapunov exponents are computed and a scaling law of the variance of their distribution is derived. Additionally, the box counting dimension as an effective dimension to characterize the fractal properties of the layer is estimated for different duration times of simulation. Its behavior in the asymptotic time limit is discussed. By computing the Lyapunov exponents and by applying methods of symbolic dynamics, the formation of the layer as a function of the external forcing strength, which in turn represents the perturbation of the originally integrable system, is characterized. In particular, it is shown that the capture of KAM tori by the layer has a remarkable influence on the averaged Lyapunov exponents. (C) 2004 Elsevier Ltd. All rights reserved},
  language  = {en}
}
@article{RaabWesselSchirdewanetal.2006,
  author    = {Raab, Corinna and Wessel, Niels and Schirdewan, Alexander and Kurths, J{\"u}rgen},
  title     = {Large-scale dimension densities for heart rate variability analysis},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.73.041907},
  year      = {2006},
  abstract  = {In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho(mu)(ls)=0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho(mu)(ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification},
  language  = {en}
}
@article{TokudaKurthsRosa2002,
  author    = {Tokuda, I. and Kurths, J{\"u}rgen and Rosa, Epaminondas},
  title     = {Learning phase synchronization from nonsynchronized chaotic regimes},
  year      = {2002},
  language  = {en}
}
@article{SchwarzSpahnGrebogietal.1999,
  author    = {Schwarz, Udo and Spahn, Frank and Grebogi, Celso and Kurths, J{\"u}rgen and Petzschmann, Olaf},
  title     = {Length scales of clustering in granular gases},
  year      = {1999},
  language  = {en}
}
@article{MarwanKurths2005,
  author    = {Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Line structures in recurrence plots},
  issn      = {0375-9601},
  year      = {2005},
  abstract  = {Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the phase-space trajectory. This provides us a better understanding of the structures occurring in recurrence plots. The relationship between the time-scales and line structures are of practical importance in cross recurrence plots. Using this relationship within cross recurrence plots, the time-scales of differently sampled or time- transformed measurements can be adjusted. An application to geophysical measurements illustrates the capability of this method for the adjustment of time-scales in different measurements. (C) 2005 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{ZiehmannSmithKurths2000,
  author    = {Ziehmann, Christine and Smith, Leonard A. and Kurths, J{\"u}rgen},
  title     = {Localized Lyapunov exponents and the prediction of predictability},
  year      = {2000},
  language  = {en}
}
@article{RosenblumPikovskijKurthsetal.2002,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen and Osipov, Grigory V. and Kiss, Istvan Z. and Hudson, J. L.},
  title     = {Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics},
  year      = {2002},
  language  = {en}
}
@article{LiChenWuetal.2009,
  author    = {Li, Ping and Chen, Maoyin and Wu, Ye and Kurths, J{\"u}rgen},
  title     = {Matrix-measure criterion for synchronization in coupled-map networks},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.79.067102},
  year      = {2009},
  abstract  = {We present conditions for the local and global synchronizations in coupled-map networks using the matrix measure approach. In contrast to many existing synchronization conditions, the proposed synchronization criteria do not depend on the solution of the synchronous state and give less limitation on the network connections. Numerical simulations of the coupled quadratic maps demonstrate the potentials of our main results.},
  language  = {en}
}
@article{GowinKurthsSaparinetal.1997,
  author    = {Gowin, W. and Kurths, J{\"u}rgen and Saparin, Peter and Felsenberg, D.},
  title     = {Measures of complexity and processing of vertebral CT-images},
  isbn      = {0-7803-4262-3},
  year      = {1997},
  language  = {en}
}
@article{ZaikinKurthsSaparinetal.2005,
  author    = {Zaikin, Alexei and Kurths, J{\"u}rgen and Saparin, Peter and Gowin, W. and Prohaska, Steffen},
  title     = {Modeling bone resorption in 2D CT and 3D mu CT images},
  issn      = {0218-1274},
  year      = {2005},
  abstract  = {We study several algorithms to simulate bone mass loss in two-dimensional and three-dimensional computed tomography bone images. The aim is to extrapolate and predict the bone loss, to provide test objects for newly developed structural measures, and to understand the physical mechanisms behind the bone alteration. Our bone model approach differs from those already reported in the literature by two features. First, we work with original bone images, obtained by computed tomography (CT); second, we use structural measures of complexity to evaluate bone resorption and to compare it with the data provided by CT. This gives us the possibility to test algorithms of bone resorption by comparing their results with experimentally found dependencies of structural measures of complexity, as well as to show efficiency of the complexity measures in the analysis of bone models. For two-dimensional images we suggest two algorithms, a threshold algorithm and a virtual slicing algorithm. The threshold algorithm simulates bone resorption on a boundary between bone and marrow, representing an activity of osteoclasts. The virtual slicing algorithm uses a distribution of the bone material between several virtually created slices to achieve statistically correct results, when the bone-marrow transition is not clearly defined. These algorithms have been tested for original CT 10 mm thick vertebral slices and for simulated 10 mm thick slices constructed from ten I mm thick slices. For three-dimensional data, we suggest a variation of the threshold algorithm and apply it to bone images. The results of modeling have been compared with CT images using structural measures of complexity in two- and three-dimensions. This comparison has confirmed credibility of a virtual slicing modeling algorithm for two-dimensional data and a threshold algorithm for three-dimensional data},
  language  = {en}
}
@article{ZaikinKurths1999,
  author    = {Zaikin, Alexei A. and Kurths, J{\"u}rgen},
  title     = {Modeling Cognitive Control in Simple Movements},
  isbn      = {1-563-96863-0},
  year      = {1999},
  language  = {en}
}
@article{LaiGrebogiKurths1999,
  author    = {Lai, Ying Cheng and Grebogi, Celso and Kurths, J{\"u}rgen},
  title     = {Modeling of deterministic chaotic systems},
  year      = {1999},
  language  = {en}
}
@article{ZaikinRosenblumScheffczyketal.1997,
  author    = {Zaikin, Alexei A. and Rosenblum, Michael and Scheffczyk, Christian and Engbert, Ralf and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen},
  title     = {Modeling qualitative changes in bimanual movements},
  year      = {1997},
  language  = {en}
}
@article{HnatkovaVesselVossetal.1998,
  author    = {Hnatkova, Katarina and Vessel, N. and Voss, Andreas and Kurths, J{\"u}rgen and Sander, A. and Schirdewan, Alexander and Camm, A. J. and Malik, Marek},
  title     = {Multiparametric analysis of heart rate variability used for risk stratification among survivors of acute myocardial infarction},
  issn      = {0895-2795},
  year      = {1998},
  language  = {en}
}
@article{KurthsKliemSchwarzetal.1998,
  author    = {Kurths, J{\"u}rgen and Kliem, Bernhard and Schwarz, Udo and Kr{\"u}ger, Albrecht and Urpo, S.},
  title     = {Multiresolution analysis of solar mm-wave bursts},
  year      = {1998},
  language  = {en}
}
@article{RomanoThielKurthsetal.2004,
  author    = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and von Bloh, Werner},
  title     = {Multivariate recurrence plots},
  issn      = {0375-9601},
  year      = {2004},
  abstract  = {We propose a new approach to calculate recurrence plots of multivariate time series, based on joint recurrences in phase space. This new method allows to estimate dynamical invariants of the whole system, like the joint Renyi entropy of second order. We use this entropy measure to quantitatively study in detail the phase synchronization of two bidirectionally coupled chaotic systems and identify different types of transitions to chaotic phase synchronization in dependence on the coupling strength and the frequency mismatch. By means of this analysis we find several new phenomena, such a chaos-period-chaos transition to phase synchronization for rather large coupling strengths. (C) 2004 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{MotterZhouKurths2005,
  author    = {Motter, Adilson E. and Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Network synchronization, diffusion, and the paradox of heterogeneity},
  issn      = {1063-651X},
  year      = {2005},
  abstract  = {Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength. Here we offer a solution to this apparent paradox. Our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states. We show that, for a given degree distribution, the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum. This enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size. Numerical verification of the main results is provided for representative classes of small-world and scale-free networks},
  language  = {en}
}
@article{KurthsSeehaferSpahn1999,
  author    = {Kurths, J{\"u}rgen and Seehafer, Norbert and Spahn, Frank},
  title     = {Nichtlineare Dynamik in der Physik : Forschungsbeispiele und Forschungstrends},
  isbn      = {3-540-65329- 5},
  year      = {1999},
  language  = {de}
}
@article{ZaikinGarciaOjalvoSchimanskyGeieretal.2002,
  author    = {Zaikin, Alexei A. and Garc{\´i}a-Ojalvo, Jordi and Schimansky-Geier, Lutz and Kurths, J{\"u}rgen},
  title     = {Noise induced propagation in monostable media},
  year      = {2002},
  abstract  = {We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium i observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits.},
  language  = {en}
}
@article{ZhouKurthsKissetal.2002,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen and Kiss, Istvan Z. and Hudson, J. L.},
  title     = {Noise-enhanced phase synchronization of chaotic oscillators},
  year      = {2002},
  language  = {en}
}
@article{BaltanasZaikinFeudeletal.2002,
  author    = {Baltan{\´a}s, J. P. and Zaikin, Alexei A. and Feudel, Fred and Kurths, J{\"u}rgen and Sanjuan, Miguel Angel Fern{\´a}ndez},
  title     = {Noise-induced effects in tracer dynamics},
  year      = {2002},
  language  = {en}
}
@article{ZhouKurths2002,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Noise-induced phase synchronization and synchronization transitions in chaotic oscillators},
  year      = {2002},
  language  = {en}
}
@article{ZhouKurths2005,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Noise-sustained and controlled synchronization of stirred excitable media by external forcing},
  issn      = {1367-2630},
  year      = {2005},
  abstract  = {Most of the previous studies on constructive effects of noise in spatially extended systems have focused on static media, e.g., of the reaction diffusion type. Because many active chemical or biological processes occur in a fluid environment with mixing, we investigate here the interplay among noise, excitability, mixing and external forcing in excitable media advected by a chaotic flow, in a two-dimensional FitzHugh-Nagumo model described by a set of reaction- advection-diffusion equations. In the absence of external forcing, noise may generate sustained coherent oscillations of the media in a range of noise intensities and stirring rates. We find that these noise-sustained oscillations can be synchronized by external periodic signals much smaller than the threshold. Analysis of the locking regions in the parameter space of the signal period, stirring rate and noise intensity reveals that the mechanism underlying the synchronization behaviour is a matching between the time scales of the forcing signal and the noise-sustained oscillations. The results demonstrate that, in the presence of a suitable level of noise, the stirred excitable media act as self-sustained oscillatory systems and become much easier to be entrained by weak external forcing. Our results may be verified in experiments and are useful to understand the synchronization of population dynamics of oceanic ecological systems by annual cycles},
  language  = {en}
}
@article{BaptistaPereiraSartorellietal.2005,
  author    = {Baptista, Murilo da Silva and Pereira, Tiago and Sartorelli, J. C. and Caldas, Ibere Luiz and Kurths, J{\"u}rgen},
  title     = {Non-transitive maps in phase synchronization},
  year      = {2005},
  abstract  = {Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{MarwanKurths2001,
  author    = {Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Nonlinear analysis of bivariate data with cross recurrence plots},
  year      = {2001},
  abstract  = {We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Nino data.},
  language  = {en}
}
@article{WesselVossMalbergetal.2000,
  author    = {Wessel, Niels and Voss, Andreas and Malberg, Hagen and Ziehmann, Christine and Voss, Henning U. and Schirdewan, Alexander and Meyerfeldt, Udo and Kurths, J{\"u}rgen},
  title     = {Nonlinear analysis of complex phenomena in cardiological data},
  year      = {2000},
  abstract  = {The main intention of this contribution is to discuss different nonlinear approaches to heart rate and blood pressure variability analysis for a better understanding of the cardiovascular regulation. We investigate measures of complexity which are based on symbolic dynamics, renormalised entropy and the finite time growth rates. The dual sequence method to estimate the baroreflex sensitivity and the maximal correlation method to estimate the nonlinear coupling between time series are employed for analysing bivariate data. The latter appears to be a suitable method to estimate the strength of the nonlinear coupling and the coupling direction. Heart rate and blood pressure data from clinical pilot studies and from very large clinical studies are analysed. We demonstrate that parameters from nonlinear dynamics are useful for risk stratification after myocardial infarction, for the prediction of life-threatening cardiac events even in short time series, and for modelling the relationship between heart rate and blood pressure regulation. These findings could be of importance for clinical diagnostics, in algorithms for risk stratification, and for therapeutic and preventive tools of next generation implantable cardioverter defibrillators.},
  language  = {en}
}
@book{KurthsMayerKress1998,
  author    = {Kurths, J{\"u}rgen and Mayer-Kress, Gottfried},
  title     = {Nonlinear analysis of physiological data},
  editor    = {Kantz, Holger},
  publisher = {Springer},
  address   = {Berlin, New York},
  isbn      = {3-540-63481-9},
  pages     = {VIII, 344 S. : Ill., graph. Darst.},
  year      = {1998},
  language  = {en}
}
@article{DongesDonnerTrauthetal.2011,
  author    = {Donges, Jonathan and Donner, Reik Volker and Trauth, Martin H. and Marwan, Norbert and Schellnhuber, Hans Joachim and Kurths, J{\"u}rgen},
  title     = {Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution},
  series = {Proceedings of the National Academy of Sciences of the United States of America},
  volume    = {108},
  journal   = {Proceedings of the National Academy of Sciences of the United States of America},
  number    = {51},
  publisher = {National Acad. of Sciences},
  address   = {Washington},
  issn      = {0027-8424},
  doi       = {10.1073/pnas.1117052108},
  pages     = {20422 -- 20427},
  year      = {2011},
  abstract  = {Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B. P.), (ii) Early Pleistocene (2.25-1.6 Ma B. P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B. P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.},
  language  = {en}
}
@article{GamezZhouTimmermannetal.2004,
  author    = {Gamez, A. J. and Zhou, Changsong and Timmermann, A. and Kurths, J{\"u}rgen},
  title     = {Nonlinear dimensionality reduction in climate data},
  issn      = {1023-5809},
  year      = {2004},
  abstract  = {Linear methods of dimensionality reduction are useful tools for handling and interpreting high dimensional data. However, the cumulative variance explained by each of the subspaces in which the data space is decomposed may show a slow convergence that makes the selection of a proper minimum number of subspaces for successfully representing the variability of the process ambiguous. The use of nonlinear methods can improve the embedding of multivariate data into lower dimensional manifolds. In this article, a nonlinear method for dimensionality reduction, Isomap, is applied to the sea surface temperature and thermocline data in the tropical Pacific Ocean, where the El Nino-Southern Oscillation (ENSO) phenomenon and the annual cycle phenomena interact. Isomap gives a more accurate description of the manifold dimensionality of the physical system. The knowledge of the minimum number of dimensions is expected to improve the development of low dimensional models for understanding and predicting ENSO},
  language  = {en}
}
@article{VossTimmerKurths2004,
  author    = {Voss, Henning U. and Timmer, Jens and Kurths, J{\"u}rgen},
  title     = {Nonlinear dynamical system identification from uncertain and indirect measurements},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples},
  language  = {en}
}
@article{WesselKleinerVossetal.1997,
  author    = {Wessel, Niels and Kleiner, H. J. and Voss, Andreas and Kurths, J{\"u}rgen and Dietz, R.},
  title     = {Nonlinear dynamics in cardiovasscular diseases},
  year      = {1997},
  language  = {en}
}
@article{ScheffczykEngbertKrampeetal.1996,
  author    = {Scheffczyk, Christian and Engbert, Ralf and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen and Rosenblum, Michael and Zaikin, Alexei A.},
  title     = {Nonlinear Modelling of Polyrhythmic Hand Movements},
  year      = {1996},
  language  = {en}
}
@article{ScheffczykEngbertKurthsetal.1995,
  author    = {Scheffczyk, Christian and Engbert, Ralf and Kurths, J{\"u}rgen and Krampe, Ralf-Thomas and Kliegl, Reinhold},
  title     = {Nonlinear Phenomena in Polyrhythmic Hand Movements},
  isbn      = {981-02-2689-6},
  year      = {1995},
  abstract  = {In this paper we apply symbolic transformations as a visualisation technique for analysing rhythm production. It is shown that qualitative information can be extracted from the experimental data. This approach may provide new insights into the organisation of temporal order by the brain on different levels of description. A simple phenomenological model for the explanation of the observed phenomena is proposed.},
  language  = {en}
}
@article{ZoellerHainzlKurths2001,
  author    = {Z{\"o}ller, Gert and Hainzl, Sebastian and Kurths, J{\"u}rgen},
  title     = {Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes},
  year      = {2001},
  language  = {en}
}
@article{LandaZaikinKurths2000,
  author    = {Landa, Polina S. and Zaikin, Alexei A and Kurths, J{\"u}rgen},
  title     = {On noise-induced transitions in nonlinear oscillators},
  isbn      = {3-540- 41074-0},
  year      = {2000},
  language  = {en}
}
@article{ZaksParkKurths2000,
  author    = {Zaks, Michael A. and Park, Eun Hyoung and Kurths, J{\"u}rgen},
  title     = {On phase synchronization by periodic force in chaotic oscillators with saddle equilibria},
  year      = {2000},
  language  = {en}
}
@article{ZaksPikovskijKurths1997,
  author    = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {On the correlation dimension of the spectral measure for the Thue-Morse sequence},
  year      = {1997},
  language  = {en}
}
@article{ZaksPikovskijKurths1999,
  author    = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {On the generalized dimensions for the fourier spectrum of the thue-morse sequence},
  year      = {1999},
  language  = {en}
}
@unpublished{WittKurthsKrauseetal.1994,
  author    = {Witt, Annette and Kurths, J{\"u}rgen and Krause, F. and Fischer, K.},
  title     = {On the validity of a model for the reversals of the Earth's magnetic field},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13460},
  year      = {1994},
  abstract  = {We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.},
  language  = {en}
}
@article{ZaikinRosenblumLandaetal.1998,
  author    = {Zaikin, Alexei A. and Rosenblum, Michael and Landa, Polina S. and Kurths, J{\"u}rgen},
  title     = {On-off itermittency phenomena in a pendulum with a randomly vibrating suspension axis},
  year      = {1998},
  language  = {en}
}
@article{ZaikinKurths2006,
  author    = {Zaikin, Alexey and Kurths, J{\"u}rgen},
  title     = {Optimal length transportation hypothesis to model proteasome product size distribution},
  series = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences},
  volume    = {32},
  journal   = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences},
  number    = {3-4},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0092-0606},
  doi       = {10.1007/s10867-006-9014-z},
  pages     = {231 -- 243},
  year      = {2006},
  abstract  = {This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport.},
  language  = {en}
}
@article{SchelterWinterhalderDahlhausetal.2006,
  author    = {Schelter, Bj{\"o}rn and Winterhalder, Matthias and Dahlhaus, Rainer and Kurths, J{\"u}rgen and Timmer, Jens},
  title     = {Partial phase synchronization for multivariate synchronizing systems},
  doi       = {10.1103/Physrevlett.96.208103},
  year      = {2006},
  abstract  = {Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated},
  language  = {en}
}
@misc{LiMeiXuetal.2020,
  author    = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf},
  title     = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {974},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47454},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-474542},
  pages     = {28},
  year      = {2020},
  abstract  = {This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the It{\^o} calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.},
  language  = {en}
}
@article{LiMeiXuetal.2020,
  author    = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf},
  title     = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity},
  series = {New Journal of Physics},
  volume    = {22},
  journal   = {New Journal of Physics},
  publisher = {Dt. Physikalische Ges.},
  address   = {Bad Honnef},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab81b9},
  pages     = {27},
  year      = {2020},
  abstract  = {This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the It{\^o} calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.},
  language  = {en}
}
@article{PikovskijRosenblumOsipovetal.1997,
  author    = {Pikovskij, Arkadij and Rosenblum, Michael and Osipov, Grigory V. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization effects in a lattice of nonidentical R{\"o}ssler oscillators},
  year      = {1997},
  language  = {en}
}
@article{RosenblumPikovskijKurths1997,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Phase synchronization in driven and coupled chaotic oscillators},
  year      = {1997},
  language  = {en}
}
@article{IvanchenkoOsipovShalfeevetal.2004,
  author    = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization in ensembles of bursting oscillators},
  issn      = {0031-9007},
  year      = {2004},
  abstract  = {We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles},
  language  = {en}
}
@article{RosenblumPikovskijKurths1997,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Phase synchronization in noisy and chaotic oscillators},
  year      = {1997},
  language  = {en}
}
@article{PikovskijRosenblumKurths2000,
  author    = {Pikovskij, Arkadij and Rosenblum, Michael and Kurths, J{\"u}rgen},
  title     = {Phase synchronization in regular and chaotic systems},
  issn      = {0218-1274},
  year      = {2000},
  language  = {en}
}
@article{ParkZaksKurths1999,
  author    = {Park, Eun Hyoung and Zaks, Michael A. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization in the forced lorenz system},
  year      = {1999},
  language  = {en}
}
@article{IvanchenkoOsipovShalfeevetal.2004,
  author    = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization of chaotic intermittent oscillations},
  issn      = {0031-9007},
  year      = {2004},
  abstract  = {We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization},
  language  = {en}
}
@article{ZaksRosenblumPikovskijetal.1997,
  author    = {Zaks, Michael A. and Rosenblum, Michael and Pikovskij, Arkadij and Osipov, Grigory V. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization of chaotic oscillations in terms of periodic orbits},
  issn      = {1054-1500},
  year      = {1997},
  language  = {en}
}
@article{RosenblumOsipovPikovskijetal.1997,
  author    = {Rosenblum, Michael and Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Phase synchronization of chaotic oscillators by external driving},
  year      = {1997},
  language  = {en}
}
@article{OsipovPikovskijKurths2002,
  author    = {Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Phase Synchronization of Chaotic Rotators},
  year      = {2002},
  abstract  = {We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor.},
  language  = {en}
}
@article{PikovskijRosenblumZaksetal.1999,
  author    = {Pikovskij, Arkadij and Rosenblum, Michael and Zaks, Michael A. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization of regular and chaotic oscillators},
  year      = {1999},
  language  = {en}
}
@unpublished{GuastiEngbertKrampeetal.2000,
  author    = {Guasti, Giovanna and Engbert, Ralf and Krampe, Ralf T. and Kurths, J{\"u}rgen},
  title     = {Phase transitions, complexity, and stationarity in the production of polyrhythms},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14933},
  year      = {2000},
  abstract  = {Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook},
  language  = {en}
}
@article{TokudaKurthsAllariaetal.2004,
  author    = {Tokuda, I. and Kurths, J{\"u}rgen and Allaria, Eugenio and Meucci, Riccardo and Boccaletti, Stefano and Arecchi, Fortunato Tito},
  title     = {Predicting phase synchronization in a spiking chaotic CO2 laser},
  issn      = {1063-651X},
  year      = {2004},
  abstract  = {An approach is presented for the reconstruction of phase synchronization phenomena in a chaotic CO2 laser from experimental data. We analyze this laser system in a regime able to phase synchronize with a weak sinusoidal forcing. Our technique recovers the synchronization diagram of the experimental system from only few measurement data sets, thus allowing the prediction of the regime of phase synchronization as well as nonsynchronization in a broad parameter space of forcing frequency and amplitude without further experiments},
  language  = {en}
}
@article{SaparinThomsenProhaskaetal.2005,
  author    = {Saparin, P. I. and Thomsen, J. S. and Prohaska, Steffen and Zaikin, Alexei and Kurths, J{\"u}rgen and Hege, H. C. and Gowin, W.},
  title     = {Quantification of spatial structure of human proximal tibial bone biopsies using 3D measures of complexity},
  issn      = {0094-5765},
  year      = {2005},
  abstract  = {Changes in trabecular bone composition during development of osteoporosis are used as a model for bone loss in microgravity conditions during a space flight. Symbolic dynamics and measures of complexity are proposed and applied to assess quantitatively the structural composition of bone tissue from 3D data sets of human tibia bone biopsies acquired by a micro-CT scanner. In order to justify the newly proposed approach, the measures of complexity of the bone architecture were compared with the results of traditional 2D bone histomorphometry. The proposed technique is able to quantify the structural loss of the bone tissue and may help to diagnose and to monitor changes in bone structure of patients on Earth as well as of the space-flying personnel. © 2005 Elsevier Ltd. All rights reserved},
  language  = {en}
}
@article{MarwanBellerFelsenbergetal.2012,
  author    = {Marwan, Norbert and Beller, Gise and Felsenberg, Dieter and Saparin, Peter and Kurths, J{\"u}rgen},
  title     = {quantifying changes in the spatial structure of trabecular bone},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {22},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {2},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127412500277},
  pages     = {12},
  year      = {2012},
  abstract  = {We apply recently introduced measures of complexity for the structural quantification of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we show how the bone may alter due to temporal immobilization.},
  language  = {en}
}
@article{ShabuninAstakhovKurths2005,
  author    = {Shabunin, A. and Astakhov, Vladimir V. and Kurths, J{\"u}rgen},
  title     = {Quantitative analysis of chaotic synchronization by means of coherence},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We use an index of chaotic synchronization based on the averaged coherence function for the quantitative analysis of the process of the complete synchronization loss in unidirectionally coupled oscillators and maps. We demonstrate that this value manifests different stages of the synchronization breaking. It is invariant to time delay and insensitive to small noise and distortions, which can influence the accessible signals at measurements. Peculiarities of the synchronization destruction in maps and oscillators are investigated},
  language  = {en}
}
@unpublished{KurthsVossWittetal.1994,
  author    = {Kurths, J{\"u}rgen and Voss, A. and Witt, Annette and Saparin, P. and Kleiner, H. J. and Wessel, Niels},
  title     = {Quantitative analysis of heart rate variability},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13470},
  year      = {1994},
  abstract  = {In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.},
  language  = {en}
}
@article{RusconiVallerianiDunlopetal.2012,
  author    = {Rusconi, Marco and Valleriani, Angelo and Dunlop, John William Chapman and Kurths, J{\"u}rgen and Weinkamer, Richard},
  title     = {Quantitative approach to the stochastics of bone remodeling},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {97},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  number    = {2},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/97/28009},
  pages     = {6},
  year      = {2012},
  abstract  = {During life bones constantly adapt their structure to their mechanical environment via a mechanically controlled process called bone remodeling. For trabecular bone, this process modifies the thickness of each trabecula leading occasionally to full resorption. We describe the irreversible dynamics of the trabecular thickness distribution (TTD) by means of a Markov chain discrete in space and time. By using thickness data from adult patients, we derive the transition probabilities in the chain. This allows a quantification, in terms of geometrical quantities, of the control of bone remodeling and thus to determine the evolution of the TTD with age.},
  language  = {en}
}