Synchronization analysis of complex dynamical networks with hybrid coupling with application to Chua’s circuit

Complex dynamic networks have been considered by researchers for their applications in modeling and analyzing many engineering issues. These networks are composed of interconnected nodes and exhibit complex behaviors that are resulted from interactions between these nodes. Synchronization, which is the concept of coordinated behavior between nodes, is the most interested behavior in these networks. This paper deals with the synchronization of complex dynamical networks with time-delays both in the states of the nodes and coupling connections between them. Moreover, constant coupling, discrete-delay coupling, and distributed-delay coupling are considered to form a hybrid coupling. Therefore, larger class and more complicated complex dynamical networks can be considered for the synchronization problem. After defining the synchronization definition, some criteria are obtained and presented in the form of linear matrix inequalities with help of the Lyapunov-Krasovskii theorem to ascertain the synchronization between each node of the network. Finally, the method is utilized for synchronization analysis of coupled Chua’s circuits which has been simulated numerically.