The Synchronization of Coupled Stochastic Systems Driven by Symmetric α-Stable Process and Brownian Motion

Abstract

The synchronization of stochastic differential equations (SDEs) driven by symmetric  -stable process and  Brownian Motion is investigated in pathwise sense. This coupled dynamical system is a new mathematical model, where one of the systems is driven by Gaussian noise, the other is driven by non-Gaussian noise. In this paper, we prove that the synchronization still persists for this coupled dynamical system. Examples and simulations are given.