Michael Rosenblum

Novgorod State University, Nowgorod, Novgorod, Russia

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Publications (123)317.1 Total impact

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    Azamat Yeldesbay, Arkady Pikovsky, Michael Rosenblum
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    ABSTRACT: We demonstrate the emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in nonlocally coupled oscillator lattices. In this regime some part of the ensemble forms a regularly evolving cluster, while all other units irregularly oscillate and remain asynchronous. We argue that the chimera emerges because of effective bistability, which dynamically appears in the originally monostable system due to internal delayed feedback in individual units. Additionally, we present two examples of chimeras in bistable systems with frequency-dependent phase shift in the global coupling.
    Physical Review Letters 04/2014; 112(14):144103. · 7.73 Impact Factor
  • Azamat Yeldesbay, Arkady Pikovsky, Michael Rosenblum
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    ABSTRACT: We demonstrate the emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in nonlocally coupled oscillator lattices. In this regime some part of the ensemble forms a regularly evolving cluster, while all other units irregularly oscillate and remain asynchronous. We argue that the chimera emerges because of effective bistability, which dynamically appears in the originally monostable system due to internal delayed feedback in individual units. Additionally, we present two examples of chimeras in bistable systems with frequency-dependent phase shift in the global coupling.
    Physical Review Letters 03/2014; 112(14). · 7.73 Impact Factor
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    Björn Kralemann, Arkady Pikovsky, Michael Rosenblum
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    ABSTRACT: We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pair-wise one. Our technique reveals effective phase connectivity which is generally not equivalent to structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.
    New Journal of Physics 02/2014; · 4.06 Impact Factor
  • Björn Kralemann, Arkady Pikovsky, Michael Rosenblum
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    ABSTRACT: We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pair-wise one. Our technique reveals effective phase connectivity which is generally not equivalent to structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.
    01/2014;
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    ABSTRACT: Internal signals like one's heartbeats are centrally processed via specific pathways and both their neural representations as well as their conscious perception (interoception) provide key information for many cognitive processes. Recent empirical findings propose that neural processes in the insular cortex, which are related to bodily signals, might constitute a neurophysiological mechanism for the encoding of duration. Nevertheless, the exact nature of such a proposed relationship remains unclear. We aimed to address this question by searching for the effects of cardiac rhythm on time perception by the use of a duration reproduction paradigm. Time intervals used were of 0.5, 2, 3, 7, 10, 14, 25, and 40 s length. In a framework of synchronization hypothesis, measures of phase locking between the cardiac cycle and start/stop signals of the reproduction task were calculated to quantify this relationship. The main result is that marginally significant synchronization indices (SIs) between the heart cycle and the time reproduction responses for the time intervals of 2, 3, 10, 14, and 25 s length were obtained, while results were not significant for durations of 0.5, 7, and 40 s length. On the single participant level, several subjects exhibited some synchrony between the heart cycle and the time reproduction responses, most pronounced for the time interval of 25 s (8 out of 23 participants for 20% quantile). Better time reproduction accuracy was not related with larger degree of phase locking, but with greater vagal control of the heart. A higher interoceptive sensitivity (IS) was associated with a higher synchronization index (SI) for the 2 s time interval only. We conclude that information obtained from the cardiac cycle is relevant for the encoding and reproduction of time in the time span of 2-25 s. Sympathovagal tone as well as interoceptive processes mediate the accuracy of time estimation.
    Frontiers in Neurorobotics 01/2014; 8:15.
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    ABSTRACT: Recovering interaction of endogenous rhythms from observations is challenging, especially if a mathematical model explaining the behaviour of the system is unknown. The decisive information for successful reconstruction of the dynamics is the sensitivity of an oscillator to external influences, which is quantified by its phase response curve. Here we present a technique that allows the extraction of the phase response curve from a non-invasive observation of a system consisting of two interacting oscillators-in this case heartbeat and respiration-in its natural environment and under free-running conditions. We use this method to obtain the phase-coupling functions describing cardiorespiratory interactions and the phase response curve of 17 healthy humans. We show for the first time the phase at which the cardiac beat is susceptible to respiratory drive and extract the respiratory-related component of heart rate variability. This non-invasive method for the determination of phase response curves of coupled oscillators may find application in many scientific disciplines.
    Nature Communications 09/2013; 4:2418. · 10.74 Impact Factor
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    ABSTRACT: Synchronization and emergence of a collective mode is a general phenomenon, frequently observed in ensembles of coupled self-sustained oscillators of various natures. In several circumstances, in particular in cases of neurological pathologies, this state of the active medium is undesirable. Destruction of this state by a specially designed stimulation is a challenge of high clinical relevance. Typically, the precise effect of an external action on the ensemble is unknown, since the microscopic description of the oscillators and their interactions are not available. We show that, desynchronization in case of a large degree of uncertainty about important features of the system is nevertheless possible; it can be achieved by virtue of a feedback loop with an additional adaptation of parameters. The adaptation also ensures desynchronization of ensembles with non-stationary, time-varying parameters. We perform the stability analysis of the feedback-controlled system and demonstrate efficient destruction of synchrony for several models, including those of spiking and bursting neurons.
    Chaos (Woodbury, N.Y.) 09/2013; 23(3):033122. · 1.80 Impact Factor
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    ABSTRACT: We perform experiments with 72 electronic limit-cycle oscillators, globally coupled via a linear or nonlinear feedback loop. While in the linear case we observe a standard Kuramoto-like synchronization transition, in the nonlinear case, with increase of the coupling strength, we first observe a transition to full synchrony and then a desynchronization transition to a quasiperiodic state. However, in this state the ensemble remains coherent so that the amplitude of the mean field is nonzero, but the frequency of the mean field is larger than frequencies of all oscillators. Next, we analyze effects of common periodic forcing of the linearly or nonlinearly coupled ensemble and demonstrate regimes when the mean field is entrained by the force whereas the oscillators are not.
    Physical Review E 06/2013; 87(6-1):062917. · 2.31 Impact Factor
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    Björn Kralemann, Arkady Pikovsky, Michael Rosenblum
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    ABSTRACT: We discuss the effect of triplet synchrony in oscillatory networks. In this state the phases and the frequencies of three coupled oscillators fulfill the conditions of a triplet locking, whereas every pair of systems remains asynchronous. We suggest an easy to compute measure, a triplet synchronization index, which can be used to detect such states from experimental data.
    Physical Review E 05/2013; 87(5-1):052904. · 2.31 Impact Factor
  • Sebastian Ehrich, Arkady Pikovsky, Michael Rosenblum
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    ABSTRACT: In most cases tendency to synchrony in networks of oscillatory units increases with the coupling strength. Using the popular Hindmarsh-Rose neuronal model, we demonstrate that even for identical neurons and simple coupling the dynamics can be more complicated. Our numerical analysis for globally coupled systems and oscillator lattices reveals a new scenario of synchrony breaking with the increase of coupling, resulting in a quasiperiodic, modulated synchronous state.
    The European Physical Journal Special Topics 01/2013; 222(10). · 1.80 Impact Factor
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    ABSTRACT: We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincaré surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled from the amplitude dynamics and provides a proper description of the phase response of chaotic oscillations. The method is illustrated with the Rössler and Lorenz systems.
    Physical Review E 02/2012; 85(2 Pt 2):026216. · 2.31 Impact Factor
  • Michael G.rosenblum, Arkady S.pikovsky, JÜrgenkurths
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    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.
    Fluctuation and Noise Letters 01/2012; 04(01). · 0.89 Impact Factor
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    ABSTRACT: We present the results of experiments with 20 electronic limit-cycle oscillators, globally coupled via a common load. We analyze collective dynamics of the ensemble in cases of linear and nonlinear phase-shifting unit in the global feedback loop. In the first case we observe the standard Kuramoto transition to collective synchrony. In the second case, we observe transition to a self-organized quasiperiodic state, predicted in [M. Rosenblum and A. Pikovsky, PRL, (2007)]. We demonstrate a good correspondence between our experimental results and previously developed theory.We also describe a simple measure which reveals the macroscopic incoherence-coherence transition in a finite??size ensemble.
    Nonlinear Dynamics of Electronic Systems, Proceedings of NDES 2012; 01/2012
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    ABSTRACT: We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett. 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.
    Physical Review E 01/2012; 85(1-2):015204. · 2.31 Impact Factor
  • Michael Rosenblum, JÜrgen Kurths
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    ABSTRACT: We would like to draw the attention of specialists in time series analysis to a simple but efficient algorithm for the determination of hidden periodic regimes in complex time series. The algorithm is stable towards additive noise and allows one to detect periodicity even if the examined data set contains only a few periods. In such cases it is more suitable than other techniques, such as spectral analysis or recurrence map. We recommend the use of this test prior to the evaluation of attractor dimensions and other dynamical characteristics from experimental data.
    International Journal of Bifurcation and Chaos 11/2011; 05(01). · 0.92 Impact Factor
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    ABSTRACT: Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time.
    Physical Review E 10/2011; 84(4 Pt 2):046201. · 2.31 Impact Factor
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    Arkady S. Pikovsky, Michael G. Rosenblum
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    ABSTRACT: In this review article we discuss effects of phase synchronization of nonlinear self-sustained oscillators. Starting with a classical theory of phase locking, we extend the notion of phase to autonoumous continuous-time chaotic systems. Using as examples the well-known Lorenz and R ö ssler oscillators, we describe the phase synchronization of chaotic oscillators by periodic external force. Both statistical and topological aspects of this phenomenon are discussed. Then we proceed to more complex cases and discuss phase synchronization in coupled systems, lattices, large globally coupled ensembles, and of space-time chaos. Finally, we demonstrate how the synchronization effects can be detected from observations of real data.
    06/2011: pages 187-219;
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    Björn Kralemann, Arkady Pikovsky, Michael Rosenblum
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    ABSTRACT: We generalize our recent approach to the reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from a multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. Partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling.
    Chaos (Woodbury, N.Y.) 06/2011; 21(2):025104. · 1.80 Impact Factor
  • Arkady Pikovsky, Michael Rosenblum
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    ABSTRACT: We consider general heterogeneous ensembles of phase oscillators, sine coupled to arbitrary external fields. Starting with the infinitely large ensembles, we extend the Watanabe–Strogatz theory, valid for identical oscillators, to cover the case of an arbitrary parameter distribution. The obtained equations yield the description of the ensemble dynamics in terms of collective variables and constants of motion. As a particular case of the general setup we consider hierarchically organized ensembles, consisting of a finite number of subpopulations, whereas the number of elements in a subpopulation can be both finite or infinite. Next, we link the Watanabe–Strogatz and Ott–Antonsen theories and demonstrate that the latter one corresponds to a particular choice of constants of motion. The approach is applied to the standard Kuramoto–Sakaguchi model, to its extension for the case of nonlinear coupling, and to the description of two interacting subpopulations, exhibiting a chimera state. With these examples we illustrate that, although the asymptotic dynamics can be found within the framework of the Ott–Antonsen theory, the transients depend on the constants of motion. The most dramatic effect is the dependence of the basins of attraction of different synchronous regimes on the initial configuration of phases.
    Physica D Nonlinear Phenomena 04/2011; 240(s 9–10):872–881. · 1.67 Impact Factor
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    Sergey P Kuznetsov, Arkady Pikovsky, Michael Rosenblum
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    ABSTRACT: We study the chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is arranged through quadratic nonlinear coupling. We show numerically that in the course of alternating Kuramoto transitions to synchrony and back to asynchrony, the exchange of excitations between two subpopulations proceeds in such a way that their collective phases are governed by an expanding circle map similar to the Bernoulli map. We perform the Lyapunov analysis of the dynamics and discuss finite-size effects.
    Chaos (Woodbury, N.Y.) 12/2010; 20(4):043134. · 1.80 Impact Factor

Publication Stats

8k Citations
317.10 Total Impact Points

Institutions

  • 2014
    • Novgorod State University
      Nowgorod, Novgorod, Russia
  • 2013
    • University of Tehran
      • School of Electrical and Computer Engineering
      Tehrān, Ostan-e Tehran, Iran
  • 2012–2013
    • Al-Farabi Kazakh National University
      Almaty, Almaty Qalasy, Kazakhstan
    • Philipps University of Marburg
      Marburg, Hesse, Germany
  • 2008–2013
    • Christian-Albrechts-Universität zu Kiel
      • Institut für Pädagogik
      Kiel, Schleswig-Holstein, Germany
  • 1995–2013
    • Universität Potsdam
      • • Institute of Physics and Astronomy
      • • Nonlinear Dynamics
      Potsdam, Brandenburg, Germany
  • 2006
    • University of Freiburg
      Freiburg, Baden-Württemberg, Germany
  • 2004
    • Humboldt-Universität zu Berlin
      Berlín, Berlin, Germany
    • University of Patras
      • Department of Medical Physics
      Patrís, Kentriki Makedonia, Greece
  • 1992–2003
    • Russian Academy of Sciences
      • Mechanical Engineering Research Institute
      Moskva, Moscow, Russia
  • 1991
    • Lomonosov Moscow State University
      • Division of Physics
      Moscow, Moscow, Russia