Identifying Topologies of Complex Dynamical Networks With Stochastic Perturbations

Abstract

Systems taking the form of networks abound in the world and attract extensive attention from the multidisciplinary nonlinear science community. As is known, network topology plays an important role in determining a network's intrinsic dynamics and function. In the past decade, many researchers have investigated the geometric features, control, and synchronization of complex networks with given or known topological structures. However, in many practical situations, the exact structure of a network is usually unknown. Therefore, inferring the intrinsic topology of complex networks is a prerequisite to understanding and explaining the evolutionary mechanisms and functional behaviors of systems built upon those networks. Furthermore, noise is ubiquitous in nature and in man-made networks. The goal of this paper is to present a simple and efficient technique to recover the underlying topologies of noise-contaminated complex dynamical networks with or without information transmission delay. The effectiveness of the approach is illustrated with a complex network composed of FHN systems. In addition, the impact of some network parameters on identification performance is further probed into.