Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks

Abstract

This paper studies noise-to-state stability in probability (NSSP) for random complex dynamical systems on networks (RCDSN). On the basis of Kirchhoff’s matrix theorem in graph theory, an appropriate Lyapunov function which combines with every subsystem for RCDSN is established. Moreover, some sufficient criteria closely related to the topological structure of RCDSN are given to guarantee RCDSN to meet NSSP by means of the Lyapunov method and stochastic analysis techniques. Finally, to show the usefulness and feasibility of theoretical findings, we apply them to random coupled oscillators on networks (RCON), and some numerical tests are given.