Synchronization in directed nonlinear complex networks under intermittent stochastic control

Abstract

Noise pervades networks and significantly influences synchronization. However, noise does not always hinder synchronization, it can actually facilitate it. This insight has led to the development of stochastic control. In this paper, an intermittent stochastic control tailored for complex networks with strongly connected topology and nonlinear dynamics is introduced, wherein noise intermittently influences the vertices. Under this control, the investigation into synchronization in complex networks is conducted. The analysis relies on algebraic graph theory and stability theory of stochastic differential equations to derive condition for network synchronization. Through rigorous derivations and simulations, it is concluded that the proposed intermittent stochastic control can achieve network synchronization, within noise playing a beneficial role. Furthermore, the study explores the impact of various features in intermittent stochastic control on synchronization, providing valuable insights for practical applications.