A new approach to partial synchronization in globally coupled rotators

Mohanty, P. K.; Politi, Antonio

doi:10.1088/0305-4470/39/26/l01

Cited by 40 publications

(35 citation statements)

References 29 publications

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“…Nevertheless, collective chaos in phase oscillators has been found only when either delayed interactions [9], multiple populations [10], or heterogeneity [11] is included in the model. Otherwise, at most macroscopic periodic oscillations arise (the so-called self-consistent partial synchrony SCPS) [12][13][14][15][16][17], the simplest setup for their observation being the biharmonic Kuramoto-Daido model [18]. The so-called balanced regime observed in the context of neural networks is, instead, an entirely different story, since the collective dynamics is basically the result of the amplification of microscopic fluctuations [19].…”

Section: Introductionmentioning

confidence: 99%

Between phase and amplitude oscillators

Clusella

Politi

2019

Phys. Rev. E

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We analyze an intermediate collective regime where amplitude oscillators distribute themselves along a closed, smooth, time-dependent curve C, thereby maintaining the typical ordering of (identical) phase oscillators. This is achieved by developing a general formalism based on two partial differential equations, which describe the evolution of the probability density along C and of the shape of C itself. The formalism is specifically developed for Stuart-Landau oscillators, but it is general enough to be applied to other classes of amplitude oscillators. The main achievements consist in: (i) identification and characterization of a new transition to selfconsistent partial synchrony (SCPS), which confirms the crucial role played by higher Fourier hamonics in the coupling function; (ii) an analytical treatment of SCPS, including a detailed stability analysis; (iii) the discovery of a new form of collective chaos, which can be seen as a generalization of SCPS and characterized by a multifractal probability density. Finally, we are able to describe given dynamical regimes both at the macroscopic as well as the microscopic level, thereby shedding further light on the relationship between the two different levels of description.

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Section: Introductionmentioning

confidence: 99%

Between phase and amplitude oscillators

Clusella

Politi

2019

Phys. Rev. E

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“…Additionally we investigate how partially synchronous states transform as neurons are made heterogeneous. To the best of our knowledge, this problem has not been addressed in previous work investigating partial synchronization in different populations of identical oscillators [29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a large system of spiking neurons with synaptic delay

2018

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We analyze a large system of heterogeneous quadratic integrate-and-fire (QIF) neurons with time delayed, all-to-all synaptic coupling. The model is exactly reduced to a system of firing rate equations that is exploited to investigate the existence, stability and bifurcations of fully synchronous, partially synchronous, and incoherent states. In conjunction with this analysis we perform extensive numerical simulations of the original network of QIF neurons, and determine the relation between the macroscopic and microscopic states for partially synchronous states. The results are summarized in two phase diagrams, for homogeneous and heterogeneous populations, which are obtained analytically to a large extent. For excitatory coupling, the phase diagram is remarkably similar to that of the Kuramoto model with time delays, although here the stability boundaries extend to regions in parameter space where the neurons are not self-sustained oscillators. In contrast, the structure of the boundaries for inhibitory coupling is different, and already for homogeneous networks unveils the presence of various partially synchronized states not present in the Kuramoto model: Collective chaos, quasiperiodic partial synchronization (QPS), and a novel state which we call modulated-QPS (M-QPS). In the presence of heterogeneity partially synchronized states reminiscent to collective chaos, QPS and M-QPS persist. In addition, the presence of heterogeneity greatly amplifies the differences between the incoherence stability boundaries of excitation and inhibition. Finally, we compare our results with those of a traditional (Wilson Cowan-type) firing rate model with time delays. The oscillatory instabilities of the traditional firing rate model qualitatively agree with our results only for the case of inhibitory coupling with strong heterogeneity. arXiv:1809.00607v2 [nlin.AO]

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“…Furthermore, quasiperiodic dynamics, when oscillators do not form any clusters and are not locked to the periodic mean field they produce, but remain, however, coherent, can be observed in homogeneous populations. Such counter-intuitive partially synchronous states have been first observed by van Vreeswijk in a model of delay-coupled integrateand-fire neurons [19], see also [20], and later in [21]. As has been shown recently, such regimes naturally appear in case of nonlinear coupling between the units [22].…”

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confidence: 62%

Controlling Collective Synchrony by Feedback

Rosenblum

Pikovsky

2008

Reviews of Nonlinear Dynamics and Complexity

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What is Collective Synchrony?Synchronization is a general nonlinear phenomenon which can be briefly described as an adjustment of rhythms of self-sustained oscillatory systems due to their interaction [1]. In the simplest setup, two periodic oscillators of this class can adjust their phases and frequencies, even if the coupling between the systems is very weak. This effect is often called phase locking or frequency entrainment. The concept can be generalized to the case of many oscillating objects with a variety of different coupling configurations: oscillating subsystems can be placed on a regular lattice, or organized in a complex, possibly irregular, network, or form a continuous medium. If an oscillating unit is interacting with its neighbors only, then synchronization typically appears in a form of waves or oscillatory modes. Contrary to this, if the interaction is a long-range one, then global synchrony, where all or almost all units oscillate in pace, can set in. Examples of synchronous dynamics range from mechanical systems like pendulum clocks [2, 3] and metronomes [4], through modern physical devices, e.g., Josephson junctions and lasers (see [5,6] and references therein) to live systems (see, e.g., a review [7]), including human beings [8,9]. The mostly popular model, describing collective dynamics in a large population of self-sustained oscillators is that of globally (all-to-all) coupled units. This framework has been used to describe many physical, biological, and social phenomena. The main effect observed in these models is the collective synchrony, when a large part or all units adjust their rhythms and produce a nonzero mean field, which has the same frequency as the synchronized majority. In the simplest setup this state appears from the fully asynchronous one via the Kuramoto transition [10,11]: if the coupling strength ε in the ensemble exceeds some threshold value ε cr , the macroscopic mean field appears and its amplitude growth with the super-criticality ε − ε cr . This transition is often considered in an analogy to second order phase transitions; on the other hand, it can be viewed at as a supercritical Hopf bifurcation for the mean field.

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A new approach to partial synchronization in globally coupled rotators

Cited by 40 publications

References 29 publications

Between phase and amplitude oscillators

Between phase and amplitude oscillators

Dynamics of a large system of spiking neurons with synaptic delay

Controlling Collective Synchrony by Feedback

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