Stochastic synchronization induced by noise

TL;DR

This paper investigates how random external impulses can synchronize oscillators' phases, revealing a stochastic regime where phase entropy fluctuates and can be controlled, with implications for understanding noise-induced synchronization.

Contribution

It introduces a stochastic framework for phase synchronization under noise, showing how entropy fluctuations characterize the transition from synchronization to erratic behavior.

Findings

Entropy of phase distributions can be tuned to negative values.

Stochastic synchronization exhibits exponential entropy distribution.

A random-walk model explains entropy dynamics and synchronization phenomena.

Abstract

Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture. The copies differ only in their arbitrary phases $\phi$. Weak, randomly-timed external impulses applied to all the copies can synchronize these phases over time. Beyond a threshold strength there is no such convergence to a common phase. Instead, the synchronization becomes erratic: successive impulses produce stochastic fluctuations in the phase distribution $q(\phi)$, ranging from near-perfect to near-random synchronization. Here we show that the sampled entropies of these phase distributions themselves form a steady-state ensemble, whose average can be made arbitrarily negative by tuning the impulse strength. A random-walk description of the entropy's evolution accounts for the observed exponential distribution of entropies and for the stochastic synchronization phenomenon.