@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}
}