Theory of frequency and phase synchronization in a rocked bistable stochastic system

TL;DR

This paper develops a new theoretical framework for understanding stochastic synchronization in a bistable system driven by noise, revealing how noise influences phase dynamics and synchronization.

Contribution

It introduces a non-Markovian renewal process approach to analyze noise-induced switching and phase synchronization in a rocked bistable system.

Findings

Analytical results agree well with numerical simulations.

Noise enhances phase synchronization in the system.

The theory extends understanding of stochastic resonance phenomena.

Abstract

We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of Stochastic Resonance. We present a new approach to the stochastic counting process of noise-induced switching events: starting from the Markovian dynamics of the nonstationary, continuous particle dynamics one finds upon contraction onto two states a non-Markovian renewal dynamics. The output frequency is determined as the velocity of the underlying discrete phase dynamics. The phenomenon of noise-assisted phase synchronization is investigated in terms of an effective, instantaneous phase diffusion. The theory is applied to rectangular-shaped rocking signals versus increasing input-noise strengths. Precise numerical simulations corroborate very favorably our analytical results. The novel theoretical findings are also compared with prior findings.