@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@unpublished{WittKurthsKrauseetal.1994,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}
}
@article{PetrovKurthsGeorgiev2003,
  author    = {Petrov, Valko and Kurths, J{\"u}rgen and Georgiev, Nikola},
  title     = {Reconstructing differential equation from a time series},
  issn      = {0218-1274},
  year      = {2003},
  abstract  = {This paper treats a problem of reconstructing ordinary differential equation from a single analytic time series with observational noise. We suppose that the noise is Gaussian (white). The investigation is presented in terms of classical theory of dynamical systems and modern time series analysis. We restrict our considerations on time series obtained as a numerical analytic solution of autonomous ordinary differential equation, solved with respect to the highest derivative and with polynomial right-hand side. In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient},
  language  = {en}
}
@unpublished{VossKurthsSchwarz1996,
  author    = {Voss, Henning and Kurths, J{\"u}rgen and Schwarz, Udo},
  title     = {Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14083},
  year      = {1996},
  abstract  = {Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record.},
  language  = {en}
}
@article{VossKurths1997,
  author    = {Voss, Henning U. and Kurths, J{\"u}rgen},
  title     = {Reconstruction of nonlinear time delay models from data by the use of optimal transformations},
  year      = {1997},
  language  = {en}
}
@article{VossKurths1999,
  author    = {Voss, Henning U. and Kurths, J{\"u}rgen},
  title     = {Reconstruction of nonlinear time-delayed feedback models from optical data},
  year      = {1999},
  language  = {en}
}
@article{RamosBuilesJaramilloPovedaetal.2017,
  author    = {Ramos, Antonio M. T. and Builes-Jaramillo, Alejandro and Poveda, German and Goswami, Bedartha and Macau, Elbert E. N. and Kurths, J{\"u}rgen and Marwan, Norbert},
  title     = {Recurrence measure of conditional dependence and applications},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {95},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.95.052206},
  pages     = {8},
  year      = {2017},
  abstract  = {Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Herewe propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.},
  language  = {en}
}
@article{MarwanSchinkelKurths2013,
  author    = {Marwan, Norbert and Schinkel, Stefan and Kurths, J{\"u}rgen},
  title     = {Recurrence plots 25 years later -Gaining confidence in dynamical transitions},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {101},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  number    = {2},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/101/20007},
  pages     = {6},
  year      = {2013},
  abstract  = {Recurrence-plot-based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots.},
  language  = {en}
}
@article{WesselMarwanMeyerfeldtetal.2001,
  author    = {Wessel, Niels and Marwan, Norbert and Meyerfeldt, Udo and Schirdewan, Alexander and Kurths, J{\"u}rgen},
  title     = {Recurrence quantification analysis to characterise the heart rate variability before the onset of ventricular tachycardia},
  year      = {2001},
  abstract  = {Ventricular tachycardia or fibrillation (VT) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this recurrence quantification analysis approach is to find early signs of sustained VT in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they are able to store at least 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study the},
  language  = {en}
}
@article{MarwanWesselMeyerfeldtetal.2002,
  author    = {Marwan, Norbert and Wessel, Niels and Meyerfeldt, Udo and Schirdewan, Alexander and Kurths, J{\"u}rgen},
  title     = {Recurrence-plot-based measures of complexity and its application to heart-rate-variability data},
  year      = {2002},
  abstract  = {The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.},
  language  = {en}
}
@article{OsipovKurths2002,
  author    = {Osipov, Grigory V. and Kurths, J{\"u}rgen},
  title     = {Regular and chaotic phase synchronization of coupled circle maps},
  year      = {2002},
  language  = {en}
}
@article{BergnerFrascaSciutoetal.2012,
  author    = {Bergner, Andre and Frasca, M. and Sciuto, G. and Buscarino, A. and Ngamga, Eulalie Joelle and Fortuna, L. and Kurths, J{\"u}rgen},
  title     = {Remote synchronization in star networks},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {85},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.85.026208},
  pages     = {7},
  year      = {2012},
  abstract  = {We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism.},
  language  = {en}
}
@article{SchwarzKurthsSpahnetal.1998,
  author    = {Schwarz, Udo and Kurths, J{\"u}rgen and Spahn, Frank and Petzschmann, Olaf},
  title     = {Reply on the comment of "Clustering of granular assemblies with temperature dependent restitution and under differential rotation"},
  year      = {1998},
  language  = {en}
}
@article{ZhouKurths2004,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Resonant patterns in noisy active media},
  issn      = {1063-651X},
  year      = {2004},
  abstract  = {We investigate noise-controlled resonant response of active media to weak periodic forcing, both in excitable and oscillatory regimes. In the excitable regime, we find that noise-induced irregular wave structures can be reorganized into frequency-locked resonant patterns by weak signals with suitable frequencies. The resonance occurs due to a matching condition between the signal frequency and the noise-induced inherent time scale of the media. m:1 resonant regions similar to the Arnold tongues in frequency locking of self-sustained oscillatory media are observed. In the self-sustained oscillatory regime, noise also controls the oscillation frequency and reshapes significantly the Arnold tongues. The combination of noise and weak signal thus could provide an efficient tool to manipulate active extended systems in experiments},
  language  = {en}
}
@article{LandaUshakovKurths2006,
  author    = {Landa, Polina S. and Ushakov, Vladimir and Kurths, J{\"u}rgen},
  title     = {Rigorous theory of stochastic resonance in overdamped bistable oscillators for weak signals},
  series = {Chaos, solitons \& fractals : applications in science and engineering},
  volume    = {30},
  journal   = {Chaos, solitons \& fractals : applications in science and engineering},
  number    = {3},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0960-0779},
  doi       = {10.1016/j.chaos.2005.08.116},
  pages     = {574 -- 578},
  year      = {2006},
  abstract  = {The results of the theoretical consideration of stochastic resonance in overdamped bistable oscillators are given. These results are founded not on the model of two states as in [McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys Rev A 1989;39:4854-69], but on splitting of motion into regular and random and the rigorous solution of the Fokker-Planck equation for the random component. We show that this resonance is caused by a change, under the influence of noise, of the system's effective stiffness and damping factor contained in the equation for the regular component. For a certain value of the noise intensity the effective stiffness is minimal, and this fact causes non-monotonic change of the output signal amplitude as the noise intensity changes. It is important that the location of the minimum and its value depend essentially on the signal frequency.},
  language  = {en}
}
@unpublished{KurthsPikovskijScheffczyk1994,
  author    = {Kurths, J{\"u}rgen and Pikovskij, Arkadij and Scheffczyk, Christian},
  title     = {Roughening interfaces in deterministic dynamics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13447},
  year      = {1994},
  abstract  = {Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.},
  language  = {en}
}
@article{HainzlZoellerKurthsetal.2000,
  author    = {Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen and Zschau, Jochen},
  title     = {Seismic quiescence as an indicator for large earthquakes in a system of self-organized criticality},
  year      = {2000},
  language  = {en}
}
@article{HainzlZoellerKurths2000,
  author    = {Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen},
  title     = {Self-organization of spatio-temporal earthquake clusters},
  year      = {2000},
  language  = {en}
}
@article{HainzlZoellerKurths1999,
  author    = {Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen},
  title     = {Self-organized criticality model for earthquakes : Quiescence, foreshocks and aftershocks},
  year      = {1999},
  language  = {en}
}
@article{WinterhalderSchelterKurthsetal.2006,
  author    = {Winterhalder, Matthias and Schelter, B and Kurths, J{\"u}rgen and Schulze-Borthage, A and Timmer, Jens},
  title     = {Sensitivity and specificity of coherence and phase synchronization analysis},
  doi       = {10.1016/j.physleta.2006.03.018},
  year      = {2006},
  abstract  = {In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{WesselZiehmannKurthsetal.2000,
  author    = {Wessel, Niels and Ziehmann, Christine and Kurths, J{\"u}rgen and Meyerfeldt, Udo and Schirdewan, Alexander and Voss, Andreas},
  title     = {Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates},
  year      = {2000},
  abstract  = {Ventricular tachycardia or fibrillation (VT-VF) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this study is to find early signs of sustained VT-VF in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they store the 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study these 1000 beat-to-beat intervals of 17 chronic heart failure ICD patients before the onset of a life-threatening arrhythmia and at a control time, i.e., without a VT-VF event. To characterize these rather short data sets, we calculate heart rate variability parameters from the time and frequency domain, from symbolic dynamics as well as the finite-time growth rates. We find that neither the time nor the frequency domain parameters show significant differences between the VT-VF and the control time series. However, two parameters from symbolic dynamics as well as the finite-time growth rates discriminate significantly both groups. These findings could be of importance in algorithms for next generation ICD's to improve the diagnostics and therapy of VT-VF.},
  language  = {en}
}
@article{ZouThielRomanoetal.2006,
  author    = {Zou, Yong and Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen and Bi, Q.},
  title     = {Shrimp structure and associated dynamics in parametrically excited oscillators},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {16},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {12},
  publisher = {World Scientific Publ. Co},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127406016987},
  pages     = {3567 -- 3579},
  year      = {2006},
  abstract  = {We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system.},
  language  = {en}
}