The synchronization, stability and stochastic resonance of stochastic global coupled system

Abstract

In this paper, we aim at a global coupled system influenced by a multiplicative dichotomous noise and an additive Gaussian white noise. Since the analysis of the synchronization and stability is important to a coupled system, and there is little general method to analyze them. We provide methods to derive the synchronization and stability of particles in the system. Guaranteed by the synchronization and stability, we obtain the analytic expression of each particle’s average displacement. To verify our results, we use stochastic Taylor expansion to derive numerical iterative expressions of the displacements of particles. As for numerical simulations, we find that the numerical solutions match the analytical solutions, and we display the synchronization speed of particles, the stable region of noise intensity, resonance areas and the output amplitude gain with respect to various parameters of the system. We find that the phenomenon of stochastic resonance occurs if and only if the parameters are situated in the resonance area.