Separatrix crossing due to multiplicative colored noise

TL;DR

This paper investigates how weak multiplicative colored noise influences Hamiltonian systems near separatrices, deriving a probability expression for noise-induced crossings and illustrating the effects with a Duffing oscillator.

Contribution

It provides a general asymptotic expression for the probability of separatrix crossing due to colored noise, highlighting the impact of noise non-linearity.

Findings

Weak colored noise can significantly alter dynamics near separatrices.

Derived a general formula for noise-induced separatrix crossing probability.

Illustrated effects using a two-well Duffing oscillator model.

Abstract

The effect of weak multiplicative colored noise on the dynamics of a Hamiltonian system is studied by means of asymptotic methods, in the vicinity of homoclinic or heteroclinic trajectories. A general expression for the probability of noise-induced separatrix crossing is obtained, and is illustrated by means of a two-well Duffing oscillator. It shows how weak noise can significantly affect the dynamics near separatrices. In addition, the influence of the degree of non-linearity of the noise amplitude is discussed.