# The effect of colored noise on heteroclinic orbits

## TL;DR

This paper analytically investigates how colored noise influences the crossing of separatrices in weakly dissipative Hamiltonian systems, revealing the roles of noise characteristics and system geometry in stochastic transitions.

## Contribution

It provides a novel analytical framework for understanding noise-induced separatrix crossing under colored noise in Hamiltonian systems.

## Key findings

- Derived the probability of noise-induced separatrix crossing analytically.
- Showed how noise intensity and correlation time affect crossing statistics.
- Applicable to a wide range of systems with small correlation time noise.

## Abstract

The dynamics of a weakly dissipative Hamiltonian system submitted to stochastic perturbations has been investigated by means of asymptotic methods. The probability of noise-induced separatrix crossing, which drastically changes the fate of the system, is derived analytically in the case where noise is an additive Kubo-Anderson process. This theory shows how the geometry of the separatrix, as well as the noise intensity and correlation time, affect the statistics of crossing. Results can be applied to a wide variety of systems, and are valid in the limit where the noise correlation time scale is much smaller than the time scale of the undisturbed Hamiltonian dynamics.