Chaos synchronization between the coupled systems on network with unknown parameters

This work investigates the adaptive network synchronization of different coupled chaotic (or hyper-chaotic) systems with unknown parameters. The definition of network synchronization is presented between the coupled systems where there are 2 N chaotic systems, the former N systems are coupled each other and so are the later N systems. Then the sufficient conditions for achieving this synchronization are derived based on the theory of the stability theory of dynamical systems with 2 N coupled chaotic systems. By the adaptive control technique, the control laws and the corresponding parameters update laws are proposed such that this network synchronization of non-identical chaotic (or hyper-chaotic) systems is to be obtained. These results obtained are in good agreement with the existing one in open literature and it is shown that the technique introduced here can be further applied to various network synchronizations between coupled dynamical systems. Finally, all our analytic results are confirmed by extensive numerical simulations of the model.