Solitary state at the edge of synchrony in ensembles with attractive and repulsive interactions

Maistrenko, Yuri; Penkovsky, Bogdan; Rosenblum, Michael G.

doi:10.1103/physreve.89.060901

Cited by 123 publications

(83 citation statements)

References 30 publications

(23 reference statements)

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“…It would also be interesting to extend the present framework towards inertia [26] and imposed phase shifts [27,28]. Finally, in small oscillator populations additional peculiarities can be expected [28]. …”

Section: Discussionmentioning

confidence: 97%

Collective dynamics in two populations of noisy oscillators with asymmetric interactions

et al. 2015

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We study two intertwined globally coupled networks of noisy Kuramoto phase oscillators that have the same natural frequency but differ in their perception of the mean field and their contribution to it. Such a give-and-take mechanism is given by asymmetric in- and out-coupling strengths which can be both positive and negative. We uncover in this minimal network of networks intriguing patterns of discordance, where the ensemble splits into two clusters separated by a constant phase lag. If it differs from π, then traveling wave solutions emerge. We observe a second route to traveling waves via traditional one-cluster states. Bistability is found between the various collective states. Analytical results and bifurcation diagrams are derived with a reduced system.

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Section: Discussionmentioning

confidence: 97%

Collective dynamics in two populations of noisy oscillators with asymmetric interactions

et al. 2015

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“…The solitary state, when a single repulsive unit leaves the synchronous cluster, was for the first time found and analyzed in Ref. 15 and later in Refs. [41][42][43][44][45] .…”

Section: Introductionmentioning

confidence: 91%

“…Our setup is an extension of the finite-size two-group Kuramoto model treated in Ref. 15 , where all oscillators were identical.…”

Section: Introductionmentioning

confidence: 99%

Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions

Teichmann

Rosenblum

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, but natural frequencies of the groups differ. In addition to a synchronous two-cluster state, the system exhibits a solitary state, when a single oscillator leaves the cluster of repulsive elements, as well as partially synchronous quasiperiodic dynamics. We demonstrate how the transitions between these states occur when the repulsion starts to prevail over attraction.PACS numbers: 05.45.Xt Synchronization; coupled oscillators Networks of coupled oscillators are a popular model for many engineered or natural systems. The main effect -emergence of a collective mode via synchronization -is now well-understood and therefore focus of research shifted recently to analysis of different complex states. These states include chimeras, when a population of identical units splits into a synchronous and asynchronous part, quasiperiodic partially synchronous states, characterized by the difference of frequencies of individual units and of the collective mode, and clusters and heteroclinic cycles, to name just a few. Of particular interest are ensembles where some elements have only attractive connections while others have only repulsive ones. This model is motivated by studies of neuronal networks that are built from excitatory and inhibitory neurons. In this paper we analyze how the state of such a setup changes with the interplay of attraction and repulsion. We demonstrate that if the frequency mismatch between attractive and repulsive units is smaller than some critical value then desynchronization occurs via appearance of the solitary state. With the further increase of repulsion the system undergoes a transition to quasiperiodic partial synchrony. In the latter state the attractive units remain synchronized, while the repulsive group settles between synchrony and asynchrony so that the mean fields of both groups remain locked, but the frequency of the repulsive elements is larger than that of their mean field. For a large frequency mismatch of attractive and repulsive groups desynchronization immediately leads to partial synchrony.

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“…Here, we show that other pattern, the so-called imperfect chimera state , which is characterized by a certain, small number of oscillators (solitary states23) which escape from the synchronized chimera's cluster or behave differently than the most of uncorrelated pendula can be observed in the networks of identical oscillators. As a proof of concept we use the network of coupled Huygens clocks24, i.e., the system of coupled pendula which are excited by the escapement clock's mechanism2526.…”

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confidence: 88%

Imperfect chimera states for coupled pendula

Kapitaniak

Kuzma

Wojewoda

et al. 2014

Sci Rep

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237

147

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The phenomenon of chimera states in the systems of coupled, identical oscillators has attracted a great deal of recent theoretical and experimental interest. In such a state, different groups of oscillators can exhibit coexisting synchronous and incoherent behaviors despite homogeneous coupling. Here, considering the coupled pendula, we find another pattern, the so-called imperfect chimera state, which is characterized by a certain number of oscillators which escape from the synchronized chimera's cluster or behave differently than most of uncorrelated pendula. The escaped elements oscillate with different average frequencies (Poincare rotation number). We show that imperfect chimera can be realized in simple experiments with mechanical oscillators, namely Huygens clock. The mathematical model of our experiment shows that the observed chimera states are controlled by elementary dynamical equations derived from Newton's laws that are ubiquitous in many physical and engineering systems.

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Solitary state at the edge of synchrony in ensembles with attractive and repulsive interactions

Cited by 123 publications

References 30 publications

Collective dynamics in two populations of noisy oscillators with asymmetric interactions

Collective dynamics in two populations of noisy oscillators with asymmetric interactions

Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions

Imperfect chimera states for coupled pendula

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