Stability analysis for stochastic complex-valued delayed networks with multiple nonlinear links and impulsive effects

This paper focuses on the stability of stochastic complex-valued delayed networks with multiple nonlinear links and impulsive effects. Different from the previous work, the links among nodes are multiple and can be nonlinear. Besides, the features of complex variables, time-varying delays and stochastic perturbations are taken into account. By utilizing complex version Itô’s formula, impulsive differential inequalities with multiple delays and graph-theoretical technique, several stability criteria are given without splitting the real and imaginary parts. These stability criteria show that if the impulsive dynamics is stable while continuous dynamics is not, it requires the dwell time of impulsive sequences to be small. Conversely, if the continuous dynamics is stable while impulsive dynamics is not, it requires the dwell time of impulsive sequences to be large. Then the theoretical results are applied to a class of stochastic complex-valued coupled oscillators. The numerical examples are carried out for demonstration purpose.