Synchronization Analysis Of A Class Complex Network With Unknown Parameters

Over the past decade, scholars in different areas of research have made extensive inquiry on complex network, which greatly promotes the vigorous development of the complex network. This paper mainly investigates the synchronization analysis of a class complex network with unknown parameters, in particular, parameters uncertainties and disturbances in complex dynamic network are deeply studied. According to different network models, the corresponding controllers are designed in different control methods. Based on the Lyapunov stability theory, we obtain the sufficient conditions for the synchronization of uncertain complex network. For different network models, several rules and algorithms are proposed to realize the expected synchronization. The effectiveness of the theory and method is verified by numerical simulation.Firstly, exponential synchronization of complex delayed dynamical network with unknown parameters is explored. Based on the Lyapunov stability theory, intermittent control method is discussed, intermittent controllers and feedback control gain are designed. Thereafter some criteria of exponential synchronization of complex delayed dynamical network with uncertain parameters are obtained. The parameter perturbation is considered, so the network model is more close to the real network. Numerical simulation examples are given to verify the validity of the proposed theory.Secondly, cluster synchronization of uncertain complex dynamic network is discussed. By designing the nonlinear controller, parameter identification and adaptive control gains, we utilize Lyapunov method and nonlinear control method to obtain the sufficient conditions for the cluster synchronization of uncertain complex network. Particularly, the network model contains a variety of unknown parameters, including external disturbance parameters, system parameters. Finally, simulation example have been presented to demonstrate the effectiveness of the theoretical result.