Study of the noise-induced transition and the exploration of the phase space for the Kuramoto–Sivashinsky equation using the minimum action method

Abstract

Noise-induced transition in the solutions of the Kuramoto–Sivashinsky (K–S) equation is investigated using the minimum action method derived from the large deviation theory. This is then used as a starting point for exploring the configuration space of the K–S equation. The particular example considered here is the transition between a stable fixed point and a stable travelling wave. Five saddle points, up to constants due to translational invariance, are identified based on the information given by the minimum action path. Heteroclinic orbits between the saddle points are identified. Relations between noise-induced transitions and the saddle points are examined.