Michael Rosenblum

Universität Potsdam, Potsdam, Brandenburg, Germany

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Publications (133)383.97 Total impact

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    Full-text · Dataset · Aug 2015
  • Michael Rosenblum · Arkady Pikovsky
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    ABSTRACT: We analyze quasiperiodic partially synchronous states in an ensemble of Stuart-Landau oscillators with global nonlinear coupling. We reveal two types of such dynamics: in the first case the time-averaged frequencies of oscillators and of the mean field differ, while in the second case they are equal, but the motion of oscillators is additionally modulated. We describe transitions from the synchronous state to both types of quasiperiodic dynamics, and a transition between two different quasiperiodic states. We present an example of a bifurcation diagram, where we show the borderlines for all these transitions, as well as domain of bistability.
    No preview · Article · Jul 2015 · Physical Review E
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    Arkady Pikovsky · Michael Rosenblum
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    ABSTRACT: In this paper we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches.
    Full-text · Article · Apr 2015 · Chaos An Interdisciplinary Journal of Nonlinear Science
  • Bjoern Kralemann · Arkady Pikovsky · Michael Rosenblum

    No preview · Conference Paper · Oct 2014
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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.
    Preview · Article · Apr 2014 · Physical Review Letters
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    Olga Pollatos · Azamat Yeldesbay · Arkady Pikovsky · Michael Rosenblum
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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.
    Full-text · Article · Apr 2014 · Frontiers in Neurorobotics
  • Azamat Yeldesbay · Arkady Pikovsky · Michael Rosenblum
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    ABSTRACT: We demonstrate emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in locally 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 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.
    No preview · Article · Mar 2014 · Physical Review Letters
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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.
    Full-text · Article · Feb 2014 · New Journal of Physics
  • 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.
    No preview · Article · Jan 2014
  • 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.
    No preview · Article · Oct 2013 · The European Physical Journal Special Topics
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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.
    Full-text · Article · Sep 2013 · Nature Communications
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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.
    Full-text · Article · Sep 2013 · Chaos (Woodbury, N.Y.)
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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.
    Full-text · Article · Jun 2013 · Physical Review E
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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.
    Full-text · Article · May 2013 · Physical Review E
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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 Poincar\'e surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled of the amplitude dynamics, and provides a proper description of phase resetting of chaotic oscillations. The method is illustrated with the R\"ossler and Lorenz systems.
    Full-text · Article · Feb 2012 · Physical Review E
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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.
    Full-text · Article · Jan 2012 · Physical Review E
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    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.
    Preview · Article · Jan 2012 · Fluctuation and Noise Letters
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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.
    Full-text · Conference Paper · Jan 2012
  • 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.
    No preview · Article · Nov 2011 · International Journal of Bifurcation and Chaos
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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.
    No preview · Article · Oct 2011 · Physical Review E

Publication Stats

13k Citations
383.97 Total Impact Points

Institutions

  • 1970-2015
    • Universität Potsdam
      • • Institute of Physics and Astronomy
      • • Nonlinear Dynamics
      Potsdam, Brandenburg, Germany
  • 1992-2011
    • Russian Academy of Sciences
      • Mechanical Engineering Research Institute
      Moskva, Moscow, Russia
  • 2004
    • Humboldt-Universität zu Berlin
      Berlín, Berlin, Germany
  • 2001
    • IMSA Amsterdam
      Amsterdamo, North Holland, Netherlands