Hybrid Synchronization Control Of Several Classes Of Complex Networks

As an important and typical dynamic behavior of complex networks,synchronization has been extensively investigated in many fields,such as physics,mathematics,information science,biology and sociology.Therefore,synchronization of complex dynamic networks is very important in theoretical and applied research.In this paper,we study the hybrid synchronization control of several classes of complex networks which are stated as follows:In the second chapter,we consider the mixed lag synchronization between two nonlinear coupling complex networks.Firstly,based on pinning control with constant feedback gain,we derive two sufficient conditions for realizing mixed lag synchronization between two networks when the feedback gain is large enough.To avoid excessive feedback gain,we give a sufficient condition which is a simple inequality involving the number of pinned nodes,the coupling strength and the feedback gain.Hence,it can be easily verified in some applications.In addition,we give a sufficient condition under the controllers based on pinning control with adaptive feedback gain.Finally,some numerical examples have been presented to illustrate the effectiveness of the theoretical results.In the third chapter,we investigate the finite-time mixed inter-layer synchronization of two-layer complex networks with unidirectional inter-layer couplings,where the drive and response layers have time-varying coupling delay and different topological structures.Based on adaptive control,a criterion for realizing the finite-time mixed inter-layer synchronization is derived.In addition,several sufficient conditions for realizing mixed inter-layer synchronization are given.Finally,some numerical simulations are presented to verify the correctness and effectiveness of theoretical results.Meanwhile,the proposed adaptive control strategy is demonstrated to be non-fragile with the noise perturbation.