Phase synchronization of switchings in stochastic and chaotic bistable systems

We study synchronization of switching processes in stochastic and chaotic b istable systems driven by a periodic signal in terms of phase synchronizati on. By introduction of instantaneous phases of transitions between metastab le states and of the periodic forcing we show explicitly the effect of phas e locking. The dynamics of phase difference appears to be qualitatively equ ivalent to that of a synchronized classical self-sustained oscillator. We h ave found that the degree of phase coherence between the input signal and t he response estimated employing the effective diffusion constant is maximal at an optimal noise level in a stochastic bistable system or at an optimal value of a control parameter in a purely deterministic case. We also consi der the effect of mutual synchronization of the switching processes in coup led stochastic and chaotic bistable systems.