Stability analysis for complex-valued stochastic delayed networks with Markovian switching and impulsive effects

This paper is concerned with the stability of complex-valued stochastic delayed networks, in which, the Markovian switching and impulsive effects are both considered into the model. Based on the existing complex version Itô’s formula and generalized Itô’s formula, we propose complex generalized Itô’s formula to study the stability of complex-valued stochastic networks with Markovian switching on complex domain directly, which avoids separating the real and imaginary parts. Then by combining Lyapunov function method with graph-theoretical technique, we derive several new sufficient conditions that mainly depend on the average impulsive interval, the connectivity of considered networks and the integral average value of the time-varying coefficients. In comparison with related results, our results are less conservative. For illustration, the stability of a class of complex-valued stochastic coupled oscillators with impulsive effects is investigated. Finally, two numerical examples are given to show the effectiveness of the main results.