Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation

In this paper, the generalized outer synchronization between two different delay-coupled complex dynamical networks with noise perturbation is investigated. With a nonlinear control scheme, the sufficient condition for almost sure generalized outer synchronization is developed based on the LaSalle-type invariance principle for stochastic differential equations. Numerical examples are examined to illustrate the effectiveness of the analytical results. The theoretic result is also applied to investigate the outer synchronization between two delay-coupled Hindmarsh–Rose neuronal networks with noise perturbation.

► We study the synchronization between two different complex networks.
► We simultaneously consider the effects of coupling delays and noise perturbation.
► In our study, two networks may have nonidentical topological structures and different node dynamics.
► Besides the numerical evidence, analytical proof of some sufficient conditions are presented.