Noise induced oscillations in non-equilibrium steady state systems

TL;DR

This paper investigates how stochastic noise influences self-organization and limit cycle stability in non-equilibrium systems, revealing conditions under which noise can induce resonance or destroy oscillations.

Contribution

It provides general expressions for noise effects on limit cycles and applies them to the stochastic Lorenz system, highlighting noise-induced resonance phenomena.

Findings

Noise can destroy limit cycles at certain scale relations.

Resonance occurs when the fastest variable couples with multiple degrees of freedom.

Departure from equilibrium steady state can be noise-induced.

Abstract

We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle at certain relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest variations displays a principle variable, which is coupled with two different degrees of freedom or more.