Generalized synchronization and their detection in the complex network with a tree topology

Abstract

In this paper, the synchronization of the complex network with nodes being nonidentical chaotic systems is studied. The master-slave synchronization scheme between unidirectionally coupled complex network nodes is solved theoretically. The generalized Lorenz system (GLS) represents each node of the complex network with different parameters. Here, the generalized synchronization in a complex network with nodes being the chaotic systems (the particular cases of the GLS, namely Lorenz and Chen chaotic systems) are studied. The application of the theoretical results for the generalized synchronization between nodes of the complex networks with tree topology is verified by the numerical simulations. The duplicated system approach is applied for the detection of the generalized synchronization in a complex network with a tree topology. The obtained results are applied to synchronize complex networks consisting of GLSs with different parameters but belong to the chaotic systems’ same class (Chen, Lorenz).