Synchronization investigation of the network group constituted by the nearest neighbor networks under inner and outer synchronous couplings**Project supported by the National Natural Science Foundation of China (Grant No. 11004092), the Natural Science Foundation of Liaoning Province, China (Grant Nos. 2015020079 and 201602455), and the Foundation of Education Department of Liaoning Province, China (Grant No. L201683665)

Abstract

A new synchronization technique of inner and outer couplings is proposed in this work to investigate the synchronization of network group. Some Haken–Lorenz lasers with chaos behaviors are taken as the nodes to construct a few nearest neighbor complex networks and those sub-networks are also connected to form a network group. The effective node controllers are designed based on Lyapunov function and the complete synchronization among the sub-networks is realized perfectly under inner and outer couplings. The work is of potential applications in the cooperation output of lasers and the communication network.