Stability of complex-valued impulsive stochastic functional differential equations on networks with Markovian switching

Abstract

This paper investigates the stability problem of complex-valued impulsive stochastic functional differential equations on networks with Markovian switching (CISFNM). Markovian switching and impulsive effects are considered into complex-valued systems for the first time. By virtue of complex generalized Itô’s formula, the stability of CISFNM can be analyzed effectively without splitting the real and imaginary parts. Then based on Razumikhin technique, graph-theoretical technique as well as average dwell-time approach, several novel stability criteria are derived, which mainly depend on integral average value of time-varying coefficients. Compared with some existing results, our results gain not only less conservativeness but also lower calculation complexity. Subsequently, the stability of complex-valued impulsive stochastic networks with time-varying delays and Markovian switching is studied. As an application, complex-valued coupled oscillators are considered and numerical simulations are also presented to show the effectiveness of our main results.