Graph Theory-Based Approach for Stability Analysis of Stochastic Coupled Systems With Levy Noise on Networks

In this paper, a novel class of stochastic coupled systems with Levy noise on networks (SCSLNNs) is presented. Both white noise and Levy noise are considered in the networks. By exploiting graph theory and Lyapunov stability theory, criteria ensuring pth moment exponential stability and stability in probability of these SCSLNNs are established, respectively. These principles are closely related to the topology of the network and the perturbation intensity of white noise and Levy noise. Moreover, to verify the theoretical results, stochastic coupled oscillators with Levy noise on a network and stochastic Volterra predator-prey system with Levy noise are performed. Finally, a numerical example about oscillators' network is provided to illustrate the feasibility of our analytical results.