Stochastic phenomena of synchronization in ensembles of mean-field coupled limit cycle oscillators with two native frequencies

Keiji Okumura, A. Ichiki, M. Shiino

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study effects of independent white noise on synchronization phenomena in ensembles of coupled limit cycle oscillators with different native frequencies. We consider a simple model where the ensemble consists of two inter-connected clusters with own native frequencies and mean-field couplings are introduced between intra- and inter-clusters. Taking advantage of the nonlinear mean-field coupling concept together with the law of large numbers valid in the thermodynamic limit, we employ a nonlinear Fokker-Planck equation approach that turns out to be a noise level-free analysis, to analytically derive the time evolution of the order parameters. Showing the occurrence of bifurcations from chaotic attractors in the deterministic limit to limit cycle ones with increasing noise intensity, we confirm the occurrence of nonequilibrium phase transitions including inter-cluster synchronization induced by external noise.

Original languageEnglish
Article number50009
JournalEurophysics Letters
Volume92
Issue number5
DOIs
Publication statusPublished - 2010 Dec
Externally publishedYes

Fingerprint

synchronism
oscillators
cycles
occurrences
noise intensity
Fokker-Planck equation
white noise
thermodynamics

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Stochastic phenomena of synchronization in ensembles of mean-field coupled limit cycle oscillators with two native frequencies. / Okumura, Keiji; Ichiki, A.; Shiino, M.

In: Europhysics Letters, Vol. 92, No. 5, 50009, 12.2010.

Research output: Contribution to journalArticle

@article{a35584119e1d4c27b9e04abc68cc9fc2,
title = "Stochastic phenomena of synchronization in ensembles of mean-field coupled limit cycle oscillators with two native frequencies",
abstract = "We study effects of independent white noise on synchronization phenomena in ensembles of coupled limit cycle oscillators with different native frequencies. We consider a simple model where the ensemble consists of two inter-connected clusters with own native frequencies and mean-field couplings are introduced between intra- and inter-clusters. Taking advantage of the nonlinear mean-field coupling concept together with the law of large numbers valid in the thermodynamic limit, we employ a nonlinear Fokker-Planck equation approach that turns out to be a noise level-free analysis, to analytically derive the time evolution of the order parameters. Showing the occurrence of bifurcations from chaotic attractors in the deterministic limit to limit cycle ones with increasing noise intensity, we confirm the occurrence of nonequilibrium phase transitions including inter-cluster synchronization induced by external noise.",
author = "Keiji Okumura and A. Ichiki and M. Shiino",
year = "2010",
month = "12",
doi = "10.1209/0295-5075/92/50009",
language = "English",
volume = "92",
journal = "EPL",
issn = "0295-5075",
publisher = "IOP Publishing Ltd.",
number = "5",

}

TY - JOUR

T1 - Stochastic phenomena of synchronization in ensembles of mean-field coupled limit cycle oscillators with two native frequencies

AU - Okumura, Keiji

AU - Ichiki, A.

AU - Shiino, M.

PY - 2010/12

Y1 - 2010/12

N2 - We study effects of independent white noise on synchronization phenomena in ensembles of coupled limit cycle oscillators with different native frequencies. We consider a simple model where the ensemble consists of two inter-connected clusters with own native frequencies and mean-field couplings are introduced between intra- and inter-clusters. Taking advantage of the nonlinear mean-field coupling concept together with the law of large numbers valid in the thermodynamic limit, we employ a nonlinear Fokker-Planck equation approach that turns out to be a noise level-free analysis, to analytically derive the time evolution of the order parameters. Showing the occurrence of bifurcations from chaotic attractors in the deterministic limit to limit cycle ones with increasing noise intensity, we confirm the occurrence of nonequilibrium phase transitions including inter-cluster synchronization induced by external noise.

AB - We study effects of independent white noise on synchronization phenomena in ensembles of coupled limit cycle oscillators with different native frequencies. We consider a simple model where the ensemble consists of two inter-connected clusters with own native frequencies and mean-field couplings are introduced between intra- and inter-clusters. Taking advantage of the nonlinear mean-field coupling concept together with the law of large numbers valid in the thermodynamic limit, we employ a nonlinear Fokker-Planck equation approach that turns out to be a noise level-free analysis, to analytically derive the time evolution of the order parameters. Showing the occurrence of bifurcations from chaotic attractors in the deterministic limit to limit cycle ones with increasing noise intensity, we confirm the occurrence of nonequilibrium phase transitions including inter-cluster synchronization induced by external noise.

UR - http://www.scopus.com/inward/record.url?scp=78650853610&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650853610&partnerID=8YFLogxK

U2 - 10.1209/0295-5075/92/50009

DO - 10.1209/0295-5075/92/50009

M3 - Article

AN - SCOPUS:78650853610

VL - 92

JO - EPL

JF - EPL

SN - 0295-5075

IS - 5

M1 - 50009

ER -