Limit cycle induced by multiplicative noise in a system of coupled Brownian motors

TL;DR

This paper investigates how multiplicative noise and global periodic coupling induce a limit cycle in a system of coupled nonlinear oscillators, revealing noise-driven oscillatory behavior beyond a critical load force.

Contribution

It demonstrates the emergence of a limit cycle caused by multiplicative noise and periodic coupling, extending previous work on noise-induced phase transitions in oscillator systems.

Findings

Existence of a noise-induced limit cycle beyond a critical load force.

Global periodic coupling and multiplicative noise jointly induce oscillatory behavior.

The system exhibits a broken-symmetry phase with noise-driven dynamics.

Abstract

We study a model consisting of $N$ nonlinear oscillators with {\em global periodic} coupling and {\em local multiplicative} and additive noises. The model was shown to undergo a nonequilibrium phase transition towards a broken-symmetry phase exhibiting noise-induced "ratchet" behavior. A previous study \cite{[7]} focused on the relationship between the character of thehysteresis loop, the number of ``homogeneous'' mean-field solutions and the shape of the stationary mean-field probability distribution function. Here we show --as suggested by the absence of stable solutions when the load force is beyond a critical value-- the existence of a limit cycle induced by both:multiplicative noise and {\em global periodic} coupling.