Synchronization of Stochastic Lévy Noise Systems on a Multi-Weights Network and Its Applications of Chua’s Circuits

Abstract

In previous work, generally, stochastic delayed coupled systems were considered on a network with a single weight. However, stochastic delayed coupled systems on a network with multi-weights have not been fully investigated and remain to be important and challenging. Hence, in this paper, time delays and Levy noise are taken into account in stochastic coupled systems on a network with multi-weights. Furthermore, synchronization of stochastic delayed coupled systems with Levy noise on a network with multi-weights (SDCSLM) is first studied via aperiodically intermittent control. Then, by means of the Lyapunov method, graph theory and some techniques of inequalities, some sufficient conditions for $p$ th moment exponential synchronization of SDCSLM are obtained. Particularly, as a practical application of the theoretical results, the exponential synchronization in mean square of stochastic Chua’s circuits with time delays and Levy noise on a network with multi-weights is studied in detail. Finally, some numerical simulations are given to show the effectiveness of the theoretical results.