Stochastic asymptotical stability for stochastic impulsive differential equations and it is application to chaos synchronization

In this paper, the stochastic asymptotical stability of stochastic impulsive differential equations is studied, and a comparison theory about the stochastic asymptotical stability of trivial solution is established. From the comparison theory, we can find out whether the stochastic impulsive differential system is stochastic asymptotically stable by studying the stability of a deterministic comparison system. As an application of this theory, we study the problem of chaos synchronization in Chua circuit using impulsive method. Finally, numerical simulation is employed to verify the feasibility of our method.

► We study the stochastic asymptotical stability of stochastic impulsive differential equations. ► A compare theory of stochastic asymptotical stability is developed. ► Chaos control of stochastic Chua circuit using impulsive method is employed to show the effectiveness of our theory. ► Stable region of stochastic Chua circuit is found under the sense of stochastic asymptotical stability.