Phase synchronization of switchings in stochastic and chaotic bistable systems

We study synchronization of switching processes in stochastic and chaotic bistable systems driven by a periodic signal in terms of phase synchronization. By introduction of instantaneous phases of transitions between metastable states and of the periodic forcing we show explicitly the effect of phase locking. The dynamics of phase difference appears to be qualitatively equivalent to that of a synchronized classical selfsustained oscillator. We have found that the degree of phase coherence between the input signal and the 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 consider the effect of mutual synchronization of the switching processes in coupled stochastic and chaotic bistable systems.