Synchronization of differential equations driven by linear multiplicative fractional Brownian motion

Abstract

This paper is devoted to the synchronization of stochastic differential equations driven by the linear multiplicative fractional Brownian motion with Hurst parameter H∈(12,1). We use equivalent transformations to prove that the differential equation has a unique stationary solution, which generates a random dynamical system. Moreover, the system has the pathwise singleton set random attractor. We then establish the synchronization of the coupled differential equations and provide numerical simulation results. At the end, we discuss two specific noise forms and present the corresponding synchronization results.