The Dynamics of Bistable Switching Behavior in Limit Cycle Systems with Additive Noise

TL;DR

This paper investigates how additive noise influences bistable switching in systems with limit cycles, revealing mechanisms that affect switching rates and directions, and explaining counter-intuitive behaviors observed in physical systems.

Contribution

It systematically analyzes the influence of vector fields on bistable switching and introduces stochastic phase reduction methods to predict switching behaviors and directions.

Findings

Noise can induce bistable switching in limit cycle systems.

Switching rates are affected by the vector field away from the limit cycle.

Systems can rotate opposite to the deterministic limit cycle due to noise.

Abstract

Additive noise is known to produce counter-intuitive behaviors in nonlinear dynamical systems. Previously, it was shown that systems with a deterministic limit cycle can display bistable switching between metastable states in the presence of asymmetric additive white noise. Here, we systematically analyze the dynamics of this bistable behavior and show how the vector field away from the limit cycle influences the rate and directionality of the bistable switching. Using stochastic phase reduction methods, we identify mechanisms underlying different rates of switching and predict when the system will rotate in the opposite direction of the deterministic limit cycle. Thus, this work presents an alternative mechanism for generating a range of bistable switch-like behaviors that have been observed in a number of physical systems.