Delay-dependent synchronization of Lévy noise coupled systems with application to Chua’s circuits

Up to now, the synchronization of stochastic delayed coupled systems with Lévy noise (SDCSL) has not been fully studied and remains to be significant and challenging. Therefore, this paper devotes to delay-dependent synchronization issue of SDCSL. Firstly, a novel global Lyapunov functional for SDCSL is given. Then, novel delay-dependent criteria are established to ensure the mean square asymptotical synchronization of SDCSL. Different from previous work about synchronization of SDCSL, the synchronization criteria are dependent on time delays in this paper, which makes our synchronization criteria less conservative than delay-independent ones. It is therefore a breakthrough in synchronization research of SDCSL. Moreover, as an application of the theoretical results, the mean square asymptotical synchronization of time delayed Chua’s circuits with Lévy noise is investigated in detail. Eventually, some numerical simulations are shown to verify the theoretical results.