@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@unpublished{VossKurthsSchwarz1996,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}
}
@article{HainzlZoellerKurths1999,
  author    = {Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen},
  title     = {Similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes},
  year      = {1999},
  language  = {en}
}
@article{ZaikinMuraliKurths2001,
  author    = {Zaikin, Alexei A. and Murali, K. and Kurths, J{\"u}rgen},
  title     = {Simple electronic circuit model for doubly stochastic resonance},
  year      = {2001},
  abstract  = {We have recently reported the phenomenon of doubly stochastic resonance [Phys. Rev. Lett. 85, 227 (2000)], a synthesis of noise-induced transition and stochastic resonance. The essential feature of this phenomenon is that multiplicative noise induces a bimodality and additive noise causes stochastic resonance behavior in the induced structure. In the present paper we outline possible applications of this effect and design a simple lattice of electronic circuits for the experimental realization of doubly stochastic resonance.},
  language  = {en}
}
@article{SchmidtZamoraLopezKurths2010,
  author    = {Schmidt, G. and Zamora-Lopez, Gorka and Kurths, J{\"u}rgen},
  title     = {Simulation of large scale cortical networks by individual neuron dynamics},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127410026149},
  year      = {2010},
  abstract  = {Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required.},
  language  = {en}
}
@unpublished{PikovskijZaksFeudeletal.1995,
  author    = {Pikovskij, Arkadij and Zaks, Michael A. and Feudel, Ulrike and Kurths, J{\"u}rgen},
  title     = {Singular continuous spectra in dissipative dynamics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13787},
  year      = {1995},
  abstract  = {We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincar{\´e} map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincar{\´e} map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.},
  language  = {en}
}
@article{FeudelJansenKurthsetal.1997,
  author    = {Feudel, Ulrike and Jansen, Wolfgang and Kurths, J{\"u}rgen and Schwarz, Udo and Voss, Henning U.},
  title     = {Solar variability : simple models and proxy data},
  isbn      = {4-274-90187-4},
  year      = {1997},
  language  = {en}
}
@article{VasconcelosLopesVianaetal.2006,
  author    = {Vasconcelos, D. B. and Lopes, S. R. and Viana, R. L. and Kurths, J{\"u}rgen},
  title     = {Spatial recurrence plots},
  doi       = {10.1103/Physreve.73.056207},
  year      = {2006},
  abstract  = {We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes},
  language  = {en}
}
@article{SunLuKurthsetal.2009,
  author    = {Sun, Xiaojuan and Lu, Qishao and Kurths, J{\"u}rgen and Wang, Qingyun},
  title     = {Spatiotemporal coherence resonance in a map lattice},
  issn      = {0218-1274},
  doi       = {10.1142/S021812740902310X},
  year      = {2009},
  abstract  = {We study the effects of parametric noise on a lattice network, which is locally modeled by a two-dimensional Rulkov map. We conclude that at some intermediate noise intensity, parametric noise can induce ordered circular patterns, which indicates the appearance of spatiotemporal coherence resonance in the studied lattice. With the observation of coherence-like manner in linear spatial cross-correlation, the coherence phenomena can be analyzed quantitatively.},
  language  = {en}
}
@article{AnishchenkoVadivasovaKopeikinetal.2003,
  author    = {Anishchenko, Vadim S. and Vadivasova, T. E. and Kopeikin, A. S. and Strelkova, G. I. and Kurths, J{\"u}rgen},
  title     = {Spectral and correlation analysis of spiral chaos},
  issn      = {0219-4775},
  year      = {2003},
  abstract  = {We study numerically the behavior of the autocorrelation function (ACF) and the power spectrum of spiral attractors without and in the presence of noise. It is shown that the ACF decays exponentially and has two different time scales. The rate of the ACF decrease is defined by the amplitude fluctuations on small time intervals, i.e., when tau < tau(cor), and by the effective diffusion coefficient of the instantantaneous phase on large time intervals. it is also demonstrated that the ACF in the Poincare map also decreases according to the exponential law exp(-lambda(+)k), where lambda(+) is the positive Lyapunov exponent. The obtained results are compared with the theory of fluctuations for the Van der Pol oscillator},
  language  = {en}
}
@article{ThielRomanoKurths2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen},
  title     = {Spurious structures in recurrence plots induced by embedding},
  doi       = {10.1007/s11071-006-2010-9},
  year      = {2006},
  abstract  = {In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay},
  language  = {en}
}
@article{KuznetsovKurths2002,
  author    = {Kuznetsov, A. S. and Kurths, J{\"u}rgen},
  title     = {Stable heteroclinic cycles for ensembles of chaotic oscillators},
  year      = {2002},
  language  = {en}
}
@article{ZakharovaVadivasovaAnishchenkoetal.2010,
  author    = {Zakharova, Anna and Vadivasova, Tatjana and Anishchenko, Vadim S. and Koseska, Aneta and Kurths, J{\"u}rgen},
  title     = {Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.81.011106},
  year      = {2010},
  abstract  = {We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.},
  language  = {en}
}
@article{VolkovUllnerKurths2005,
  author    = {Volkov, E. I. and Ullner, Ekkehard and Kurths, J{\"u}rgen},
  title     = {Stochastic multiresonance in the coupled relaxation oscillators},
  issn      = {1054-1500},
  year      = {2005},
  abstract  = {We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh- Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have different average periods distinct from that of an isolated oscillator and various phase relations between the elements. We explain the correspondence between the noise-supported stochastic attractors and the observed resonance peaks in the curves for the linear response versus signal frequency. (C) 2005 American Institute of Physics},
  language  = {en}
}
@article{ZemanovaZhouKurths2006,
  author    = {Zemanova, Lucia and Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Structural and functional clusters of complex brain networks},
  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.2006.09.008},
  pages     = {202 -- 212},
  year      = {2006},
  abstract  = {Recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. It is of importance to understand the implications of such complex network structures in the functional organization of the brain activities. Here we study this problem from the viewpoint of dynamical complex networks. We investigate synchronization dynamics on the corticocortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behavior, and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.},
  language  = {en}
}
@article{AnishchenkoKopeikinKurths2000,
  author    = {Anishchenko, Vadim S. and Kopeikin, A. S. and Kurths, J{\"u}rgen},
  title     = {Studying hyperbolicity in chaotic systems},
  year      = {2000},
  language  = {en}
}
@article{ThielRomanoSchwarzetal.2004,
  author    = {Thiel, M. and Romano, Maria Carmen and Schwarz, Udo and Kurths, J{\"u}rgen and Timmer, Jens},
  title     = {Surrogate-based hypothesis test without surrogates},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1},
  language  = {en}
}
@article{ZaksPikovskijKurths1998,
  author    = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Symbolic dynamics behind the singular continuous power spectra of continuous flows},
  year      = {1998},
  language  = {en}
}
@article{WesselSchwarzSaparinetal.2002,
  author    = {Wessel, Niels and Schwarz, Udo and Saparin, Peter and Kurths, J{\"u}rgen},
  title     = {Symbolic dynamics for medical data analysis},
  isbn      = {3-936142-09-2},
  year      = {2002},
  abstract  = {Observational data of natural systems, as measured in medical measurements are typically quite different from those obtained in laboratories. Due to the peculiarities of these data, wellknown characteristics, such as power spectra or fractal dimension, often do not provide a suitable description. To study such data, we present here some measures of complexity, which are basing on symbolic dynamics. Firstly, a motivation for using symbolic dynamics and measures of complexity in data analysis based on the logistic map is given and next, two applications to medical data are shown. We demonstrate that symbolic dynamics is a useful tool for the risk assessment of patients after myocardial infarction as well as for the evaluation of th e architecture of human cancellous bone.},
  language  = {en}
}
@article{EngbertScheffczykKrampeetal.2002,
  author    = {Engbert, Ralf and Scheffczyk, Christian and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen and Kliegl, Reinhold},
  title     = {Symbolic dynamics of bimanual production of polyrhythms},
  isbn      = {3-540- 63481-9},
  year      = {2002},
  abstract  = {We analyse time series from a study on bimanual rhythmic movements in which the speed of performance (the external control parameter) was experimentally manipulated. Using symbolic transformations as a visualization technique we observe qualitative changes in the dynamics of the timing patterns. Such phase transitions are quantitatively described by measures of complexity. Using these results we develop an advanced symbolic coding which enables us to detect important dynamical structures. Furthermore, our analysis raises new questions concerning the modelling of the underlying human cognitive-motor system.},
  language  = {en}
}
@article{SchiekScheffczykEngbertetal.1997,
  author    = {Schiek, Michael and Scheffczyk, Christian and Engbert, Ralf and Kurths, J{\"u}rgen and Krampe, Ralf-Thomas and Kliegl, Reinhold and Drepper, Friedhelm R.},
  title     = {Symbolic dynamics of physiological synchronisation : examples from bimanual movements and cardiorespiratory interaction},
  year      = {1997},
  abstract  = {Key words: Nonlinear time series analysis, symbolic dynamics, phase transitions, physiological data, biological synchronization, production of polyrhythms, cardiorespiratory interaction, variation of control parameter},
  language  = {en}
}
@book{PikovskijRosenblumKurths2001,
  author    = {Pikovskij, Arkadij and Rosenblum, Michael and Kurths, J{\"u}rgen},
  title     = {Synchronization : a universal concept in nonlinear sciences},
  series = {Cambridge nonlinear science series},
  volume    = {12},
  journal   = {Cambridge nonlinear science series},
  edition   = {1st paperback ed., repr},
  publisher = {Cambridge Univ. Press},
  address   = {Cambridge},
  isbn      = {0-521-59285-2},
  pages     = {XIX, 411 S. : Ill., graph. Darst.},
  year      = {2001},
  language  = {en}
}
@article{KurthsRomanoThieletal.2006,
  author    = {Kurths, J{\"u}rgen and Romano, Maria Carmen and Thiel, Marco and Osipov, Grigory V. and Ivanchenko, Mikhail V. and Kiss, Istvan Z. and Hudson, John L.},
  title     = {Synchronization analysis of coupled noncoherent oscillators},
  issn      = {0924-090X},
  doi       = {10.1007/s11071-006-1957-x},
  year      = {2006},
  abstract  = {We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators},
  language  = {en}
}
@article{RosenblumPikovskijKurths2004,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Synchronization approach to analysis of biological systems},
  issn      = {0219-4775},
  year      = {2004},
  abstract  = {In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss the potentials as well as limitations and misinterpretations of the approach},
  language  = {en}
}
@article{BoccalettiHwangChavezetal.2006,
  author    = {Boccaletti, Stefano and Hwang, Dong-Uk and Chavez, Mario and Amann, Andreas and Kurths, J{\"u}rgen and Pecora, Louis M.},
  title     = {Synchronization in dynamical networks : evolution along commutative graphs},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.74.016102},
  year      = {2006},
  abstract  = {Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior},
  language  = {en}
}
@article{RosenblumKurthsPikovskijetal.1998,
  author    = {Rosenblum, Michael and Kurths, J{\"u}rgen and Pikovskij, Arkadij and Schafer, C. and Tass, Peter and Abel, Hans-Henning},
  title     = {Synchronization in Noisy Systems and Cardiorespiratory Interaction},
  year      = {1998},
  language  = {en}
}
@article{RosenblumAbelKurthsetal.1999,
  author    = {Rosenblum, Michael and Abel, Hans-Henning and Kurths, J{\"u}rgen and Sch{\"a}fer, Carsten},
  title     = {Synchronization in the human cardiorespiratory system},
  year      = {1999},
  language  = {en}
}
@article{HuangChenKurths2011,
  author    = {Huang, Tingwen and Chen, Guanrong and Kurths, J{\"u}rgen},
  title     = {Synchronization of chaotic of chaotic systems with time-varying coup{\"o}ing delays},
  series = {Discrete and continuous dynamical systems : a journal bridging mathematics and sciences ; Series B, Mathematical modelling, analysis and computations},
  volume    = {16},
  journal   = {Discrete and continuous dynamical systems : a journal bridging mathematics and sciences ; Series B, Mathematical modelling, analysis and computations},
  number    = {4},
  publisher = {American Institute of Mathematical Sciences},
  address   = {Springfield},
  issn      = {1531-3492},
  doi       = {10.3934/dcdsb.2011.16.1071},
  pages     = {1071 -- 1082},
  year      = {2011},
  abstract  = {In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation in equalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method.},
  language  = {en}
}
@article{BoccalettiValladaresKurths2000,
  author    = {Boccaletti, Stefano and Valladares, D. L. and Kurths, J{\"u}rgen},
  title     = {Synchronization of chaotic structurally nonequivalent systems},
  year      = {2000},
  language  = {en}
}
@article{LiSunKurths2006,
  author    = {Li, Changpin and Sun, Weigang and Kurths, J{\"u}rgen},
  title     = {Synchronization of complex dynamical networks with time delays},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2005.07.007},
  year      = {2006},
  abstract  = {In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in Such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems.},
  language  = {en}
}
@article{MeucciSalvadoriIvanchenkoetal.2006,
  author    = {Meucci, Riccardo and Salvadori, Francesco and Ivanchenko, Mikhail V. and Al Naimee, Kais and Zhou, Chansong and Arecchi, Fortunato Tito and Boccaletti, Stefano and Kurths, J{\"u}rgen},
  title     = {Synchronization of spontaneous bursting in a CO2 laser},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {74},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.74.066207},
  pages     = {6},
  year      = {2006},
  abstract  = {We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.},
  language  = {en}
}
@article{MontbrioKurthsBlasius2004,
  author    = {Montbrio, Ernest and Kurths, J{\"u}rgen and Blasius, Bernd},
  title     = {Synchronization of two interacting populations of oscillators},
  year      = {2004},
  abstract  = {We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed.},
  language  = {en}
}