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

Shahad Al-Azzawi, Jicheng Liu, Xianming Liu

The synchronization of stochastic differential equations (SDEs) driven by symmetric α-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, another one 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.