Two scenarios for the onset and suppression of collective oscillations in heterogeneous populations of active rotators

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dc.citation.issue6
dc.citation.rankM21
dc.citation.spage062211
dc.citation.volume100
dc.contributor.authorKlinshov, Vladimir
dc.contributor.authorFranović, Igor
dc.date.accessioned2024-06-20T11:16:21Z
dc.date.available2024-06-20T11:16:21Z
dc.date.issued2019-12-27
dc.description.abstractWe consider the macroscopic regimes and the scenarios for the onset and the suppression of collective oscillations in a heterogeneous population of active rotators composed of excitable or oscillatory elements. We analyze the system in the continuum limit within the framework of Ott-Antonsen reduction method, determining the states with a constant mean field and their stability boundaries in terms of the characteristics of the rotators' frequency distribution. The system is established to display three macroscopic regimes, namely the homogeneous stationary state, where all the units lie at the resting state, the global oscillatory state, characterized by the partially synchronized local oscillations, and the heterogeneous stationary state, which includes a mixture of resting and asynchronously oscillating units. The transitions between the characteristic domains are found to involve a complex bifurcation structure, organized around three codimension-two bifurcation points: A Bogdanov-Takens point, a cusp point, and a fold-homoclinic point. Apart from the monostable domains, our study also reveals two domains admitting bistable behavior, manifested as coexistence between the two stationary solutions or between a stationary and a periodic solution. It is shown that the collective mode may emerge via two generic scenarios, guided by a saddle-node of infinite period or the Hopf bifurcation, such that the transition from the homogeneous to the heterogeneous stationary state under increasing diversity may follow the classical paradigm, but may also be hysteretic. We demonstrate that the basic bifurcation structure holds qualitatively in the presence of small noise or small coupling delay, with the boundaries of the characteristic domains shifted compared to the noiseless and the delay-free case.
dc.identifier.doi10.1103/physreve.100.062211
dc.identifier.issn2470-0045
dc.identifier.issn2470-0053
dc.identifier.scopus2-s2.0-85077438917
dc.identifier.urihttps://pub.ipb.ac.rs/handle/123456789/127
dc.identifier.wos000504640700002
dc.language.isoen
dc.publisherAmerican Physical Society (APS)
dc.relation.ispartofPhysical Review E
dc.relation.ispartofabbrPhys. Rev. E
dc.rightsrestrictedAccess
dc.titleTwo scenarios for the onset and suppression of collective oscillations in heterogeneous populations of active rotators
dc.typeArticle
dc.type.versionpublishedVersion
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