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

TL;DR

This paper investigates how independent white noise influences synchronization in coupled limit cycle oscillators with two native frequencies, revealing noise-induced phase transitions and bifurcations from chaos to order.

Contribution

It introduces an analytical approach using nonlinear Fokker-Planck equations to study noise effects on synchronization in multi-cluster oscillator ensembles.

Findings

Noise induces bifurcations from chaos to limit cycles.

External noise can cause inter-cluster synchronization.

Phase transitions are driven by noise intensity.

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 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 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.