Analytic description of noise-induced phase synchronization

¹ Institute of Physics, Humboldt-University at Berlin Invalidenstr. 110, D-10115, Berlin, Germany
² Center for Neurodynamics, University of Missouri at St. Louis St. Louis, MO 63121, USA

Received: 26 November 1999
Accepted: 27 January 2000

Abstract

We study the phase synchronization of a noisy bistable system with an external dichotomic signal of either periodic or Markovian character. Using a generic two-state model, a basic paradigm of stochastic resonance, we analytically prove the occurrence of noise-induced frequency and effective phase locking characterized by a plateau of the mean output switching rate and a minimum of the phase difference diffusivity, respectively. The first phenomenon characterizes the entrainment of the mean output frequency by periodic and even by aperiodic switching events. The second one constitutes a much more comprehensive effect: The average duration of phase locking episodes between input and output, which is connected with the phase difference diffusion coefficient, increases enormously for optimally selected noise, thus justifying the notion of effective phase-synchronization.