@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{DanaBlasiusKurths2006,
  author    = {Dana, Syamal Kumar and Blasius, Bernd and Kurths, J{\"u}rgen},
  title     = {Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators},
  issn      = {1054-1500},
  doi       = {10.1063/1.2197168},
  year      = {2006},
  abstract  = {We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models},
  language  = {en}
}
@article{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{BaptistaPereiraKurths2006,
  author    = {Baptista, Murilo da Silva and Pereira, Tiago and Kurths, J{\"u}rgen},
  title     = {Upper bounds in phase synchronous weak coherent chaotic attractors},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2006.02.007},
  year      = {2006},
  abstract  = {An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map.},
  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{KitajimaKurths2005,
  author    = {Kitajima, H. and Kurths, J{\"u}rgen},
  title     = {Synchronized firing of FitzHugh-Nagumo neurons by noise},
  issn      = {1054-1500},
  year      = {2005},
  abstract  = {We investigate the influence of noise on synchronization between the spiking activities of neurons with external impulsive forces. We first analyze the dependence of the synchronized firing on the amplitude and the angular frequency of the impulsive force in the noise-free system. Three cases (regular spiking, traveling wave, and chaotic spiking) with low synchronized firing are chosen to study effects due to noise. In each case we find that small noise can be a promoter of synchronization phenomena in neural activities, by choosing an appropriate noise intensity acting on some of the neurons. (C) 2005 American Institute of Physics},
  language  = {en}
}
@article{BeimGrabenFrischFinketal.2005,
  author    = {Beim Graben, Peter and Frisch, Stefan and Fink, A. and Saddy, Douglas and Kurths, J{\"u}rgen},
  title     = {Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We apply the recently developed symbolic resonance analysis to electroencephalographic measurements of event- related brain potentials (ERPs) in a language processing experiment by using a three-symbol static encoding with varying thresholds for analyzing the ERP epochs, followed by a spin-flip transformation as a nonlinear filter. We compute an estimator of the signal-to-noise ratio (SNR) for the symbolic dynamics measuring the coherence of threshold-crossing events. Hence, we utilize the inherent noise of the EEG for sweeping the underlying ERP components beyond the encoding thresholds. Plotting the SNR computed within the time window of a particular ERP component (the N400) against the encoding thresholds, we find different resonance curves for the experimental conditions. The maximal differences of the SNR lead to the estimation of optimal encoding thresholds. We show that topographic brain maps of the optimal threshold voltages and of their associated coherence differences are able to dissociate the underlying physiological processes, while corresponding maps gained from the customary voltage averaging technique are unable to do so},
  language  = {en}
}
@article{MeineckeZieheKurthsetal.2005,
  author    = {Meinecke, Frank C. and Ziehe, Andreas and Kurths, J{\"u}rgen and M{\"u}ller, Klaus-Robert},
  title     = {Measuring phase synchronization of superimposed signals},
  issn      = {0031-9007},
  year      = {2005},
  abstract  = {Phase synchronization is an important phenomenon that occurs in a wide variety of complex oscillatory processes. Measuring phase synchronization can therefore help to gain fundamental insight into nature. In this Letter we point out that synchronization analysis techniques can detect spurious synchronization, if they are fed with a superposition of signals such as in electroencephalography or magnetoencephalography data. We show how techniques from blind source separation can help to nevertheless measure the true synchronization and avoid such pitfalls},
  language  = {en}
}
@article{SurovyatkinaKravtsovKurths2005,
  author    = {Surovyatkina, E. D. and Kravtsov, Y. A. and Kurths, J{\"u}rgen},
  title     = {Fluctuation growth and saturation in nonlinear oscillators on the threshold of bifurcation of spontaneous symmetry breaking},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We study prebifurcation fluctuation amplification in nonlinear oscillators subject to bifurcations of spontaneous symmetry breaking which are manifest in the doubling of stable equilibrium states. Our theoretical estimates of both the linear growth and the nonlinear saturation of the fluctuations are in good agreement with our results from numerical simulations. We show that in the saturation mode, the fluctuation variance is proportional to the standard deviation of the external noise, whereas in the linear mode, the fluctuation variance is proportional to the noise variance. It is demonstrated that the phenomenon of prebifurcation noise amplification is more pronounced in the case of a slow transition through the bifurcation point. The amplification of fluctuations in this case makes it easier to form a symmetric probability of the final equilibrium states. In contrast, for a fast transition through the bifurcation point, the effect of amplification is much less pronounced. Under backward and forward passages through the bifurcation point, a loop of noise-dependent hysteresis emerges here. We find that for a fast transition of the nonlinear oscillator through the bifurcation point, the probability symmetry of the final equilibrium states is destroyed},
  language  = {en}
}
@article{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}
}