Synchronization analysis of stochastic coupled systems with time delay on networks by periodically intermittent control and graph-theoretic method

In this paper, the issue of inner exponential synchronization (IES) for a class of stochastic coupled systems with time-varying delay on networks (SCSTVDNs) is investigated. A periodically intermittent control strategy is introduced to drive such SCSTVDNs to achieve IES. By exploiting Lyapunov method and Kirchhoffs matrix tree theorem in graph theory, two types of sufficient IES criteria are respectively established in the form of Lyapunov-type theorem and coefficients-type theorem. Furthermore, to show the practicability of the theoretical results, the analysis of IES for the second-order Kuramoto oscillators with stochastic perturbations and time-varying delay is performed. A numerical example is finally provided to demonstrate the validity and feasibility of our analytical results.