Stochastic transitions through unstable limit cycles in a model of bistable thermochemical system

Abstract

The master equation approach is used to study transitions through an unstable limit cycle surrounding a stable focus in two-variable systems with three stationary states. The model considered describes a bistable thermochemical system. Two cases are studied. In the first one transitions occur from a basin of attraction of a stable limit cycle to a basin of attraction of a stable focus surrounded by an unstable limit cycle. In the second case, stochastic trajectories cross the unstable limit cycle going from a basin of attraction of a stable node to a basin of attraction of a stable focus. Distribution functions of the first passage time between these attractors are calculated and discussed for systems with various numbers of particles. The distribution functions in both cases exhibit a multi-peak character. A fine structure of single peaks is observed in the first case.