Switching barrier scaling near bifurcation points for non-Gaussian noise

TL;DR

This paper investigates how non-Gaussian noise, specifically Poisson noise, affects the rate of noise-induced switching near bifurcation points, revealing a non-power-law dependence and the dominance of Gaussian noise close to bifurcations.

Contribution

It introduces a detailed analysis of switching exponents under non-Gaussian noise near bifurcations, highlighting the crossover with Gaussian noise influence.

Findings

Switching exponent exhibits non-power-law dependence on bifurcation proximity for Poisson noise.

Weak Gaussian noise dominates switching behavior very close to bifurcation points.

Crossover behavior occurs between non-Gaussian and Gaussian noise effects near bifurcations.

Abstract

We study noise-induced switching of a system close to bifurcation parameter values where the number of stable states changes. For non-Gaussian noise, the switching exponent, which gives the logarithm of the switching rate, displays a non-power-law dependence on the distance to the bifurcation point. This dependence is found for Poisson noise. Even weak additional Gaussian noise dominates switching sufficiently close to the bifurcation point, leading to a crossover in the behavior of the switching exponent.