Stability of multi-links complex-valued impulsive stochastic systems with Markovian switching and multiple delays

Abstract

This paper considers the stability and existence of multi-links complex-valued impulsive stochastic nonlinear coupled systems with Markovian switching and multiple time-varying delays. The complex-valued Itô formula not only avoids separating the real and imaginary parts but also considers the stability and existence of multi-links complex-valued stochastic coupled systems with Markovian switching. Through the Lyapunov function of the vertex systems and graph theory techniques, the method of constructing the Lyapunov function of the networks is given. With the help of this method, the criteria for achieving p-th exponential stability are obtained, which is related to the average impulsive interval Ta and the connectivity of the networks. In addition, considering that the existence of solutions for stochastic systems with Markovian switching may be affected, through the combination of graph-theoretical technique and the Lyapunov function and the principle of contraction mapping, we get the conditions to guarantee the existence of solutions, which are also related to Ta and the connectivity of the networks. To verify the validity of the theoretical results, we consider a class of multi-links impulsive stochastic coupled neural networks with Markovian switching and multiple time-varying delays and give two numerical examples to verify the validity of the main results.