Research On Improved Synchronization Control For Complex Networks With Parameters Uncertainty

Nonlinear systems are ubiquitous in nature and real life.Complex nonlinear phenomena arise in many systems due to internal topological connections and nonlinear effects,such as power networks,transportation networks,computer networks,neural networks,social networks,etc.The complex network is an abstract mathematical model used to describe such nonlinear systems.The dynamics of the network describes the process by which the state of nodes themselves and the connections between nodes change under external disturbances and internal actions.Synchronization of complex networks is an evolutionary process in which the dynamic characteristics of different nodes of the system tend to be the same which is closely related to the topology of the network and the coupling strength of the nodes.The research on the synchronization stability of complex networks is helpful to understand the operation mechanism of the system.Due to the ubiquity of time delays,introducing time delays in complex network models can better describe the network structure and approximate the new actual system.In view of this,based on the existing time-delay complex network model,this paper obtains two more general mixed two-delay complex network models by adding node delay and coupling time delays.For the linear coupling time-delay complex network model,the improved function projective synchronization problem of two complex networks with the same structure under uncertain parameters is considered.Based on Lyapunov stability theory,a mixed control composed of nonlinear feedback control and adaptive control is proposed.Moreover,sufficient conditions for the synchronization of the drive-response system are given,and the stability of the synchronization is verified.For the nonlinear coupling time-delay complex network model,the finite-time synchronization problem of two complex networks with different structures under uncertain parameters is considered.Based on the finite-time stability theory,a nonlinear feedback control independent of timedelay is proposed.Similarly,sufficient conditions for the synchronization of the drive-response system are given and the stability of the synchronization is verified.Finally,the effectiveness of the control method is verified by numerical simulation for the two synchronous control systems given above.