An analytical proof for synchronization of stochastic phase oscillator

Abstract

In this paper, we show that under a generic condition of the coefficient of a stochastic phase oscillator the Lyapunov exponent of the linearization along an arbitrary solution is always negative. Consequently, the generated random dynamical system exhibits a synchronization.

References in corpus (2)

• Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
• Phase reduction of stochastic limit cycle oscillators