Effects of noise on synchronization phenomena exhibited by mean-field coupled limit cycle oscillators with two natural frequencies

TL;DR

This paper analyzes how external white Gaussian noise influences synchronization in mean-field coupled limit cycle oscillators with two natural frequencies, revealing noise-induced phase transitions and bifurcations.

Contribution

It introduces an analytical approach using nonlinear Fokker-Planck equations to study noise effects on synchronization in a mean-field oscillator model with two frequencies.

Findings

Noise induces inter-cluster synchronization.

Bifurcations from chaos to limit cycles occur with increasing noise.

Nonequilibrium phase transitions are confirmed.

Abstract

Relationships between inter-cluster synchronization phenomena and external noise are studied on the basis of noise level-free analysis. We consider a mean-field model of ensembles of coupled limit cycle oscillators with two natural frequencies, which are subjected to external white Gaussian noise. Using a nonlinear Fokker-Planck equation approach, we analytically derive the order parameter equations associated with nonequilibrium phase transitions in the thermodynamic limit. Solving them numerically, we systematically investigate the model parameter dependences of the appearance and disappearance of synchronization phenomena. Demonstrating bifurcations from chaotic attractors in the deterministic limit to limit cycle attractors with increasing noise intensity, we confirm the occurrence of nonequilibrium phase transitions including inter-cluster synchronization induced by external white Gaussian noise.