Global Synchronization of Complex Networks Perturbed by Brown Noises and Poisson Noises

Stochastic disturbances, such as Brown noises and Poisson noises, are ubiquitous in the real world. It is necessary to consider these noises' effect for dynamical behaviors of complex networks. This paper addresses the synchronization problem for complex networks perturbed by Brown noises and Poisson noises. By utilizing the martingale theory such as the predictable projection operator and the dual predictable projection operator, we transform the expectation of the stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper presents a global synchronization criterion for complex networks perturbed by Brown noises and Poisson noises. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed approach.