Stochastic distribution synchronization and pinning control for complex heterogeneous dynamical networks

Abstract

AbstractThis paper investigates the stochastic synchronization and pinning control in the sense of probability distribution for a general model of complex heterogeneous dynamical networks subjected to stochastic disturbances. Some generic stochastic synchronization criteria are established for both cases of undirected and directed topology by using the ergodic theory on stochastic dynamical systems. Compared with most existing studies on the stochastic synchronization in the sense of mean square, it is demonstrated that the concept of stochastic distribution synchronization can well characterize the realistic structure and essential nature of complex practical stochastic systems. Subsequently, two representative examples of complex heterogeneous dynamical networks, namely coupled stochastic Duffing oscillators and coupled FitzHugh‐Nagumo neuron oscillators, are given to illustrate and numerically verify the theoretical results.