Complex Network Synchronization Control And Analysis Based On Fractional Order Controller

With the development of information technology,complex network has been widely used to describe a variety of artificial and natural systems,such as social network,the Internet,neural network and biological network.Complex network is one of the key research topics in the 21st century,attracting a large number of researchers in different fields,and researchers have established some classic network models to describe all kinds of real complex systems in real life.Research deeply on complex network is of great significance to better understand the all kinds of real complex systems.Synchronization,as the main dynamic behavior of complex network,has been favored by researchers.The early research of complex network synchronization is only for the node which is the integer order differential system,and the fractional differential system can better describe the memory attribute in the real network,therefore,synchronization control and research of fractional order complex network has become a new research subject.Based on Lyapunov stability theory,nonlinear fractional order stability theory and LaSalle invariance principle,the hybrid synchronization problem of two coupled fractional order complex networks is studied in this thesis.By introducing a fractional-order controller,two coupled complex networks with fractional-order chaotic or hyper-chaotic nodes achieve hybrid synchronization state.Sufficient conditions for hybrid synchronization which include the outer synchronization between the driving and response networks and inner synchronization in each network are proposed.Theoretical analysis and simulation experiments verify that,if the system parameters satisfy the specific conditions,two coupled networks can reach the hybrid synchronization.In addition,this thesis focuses on projective synchronization problem of two coupled fractional order complex networks with fractional order chaotic system.By using the nonlinear fractional-order stability theory and the adaptive control strategy,a fractional order controller is added to the response network to reach projective synchronization of driving-response networks.The following is the main content and innovations of the thesis:(1)Using the definition of fractional calculus,complex network consisting of fractional order differential systems is deeply studied.In the synchronization analysis for fractional order complex network,considering the influence of order on the control effect of the system,the controller in which the control parameter is the fractional order differential form is selected and the validity of the controller is verified by experiments.(2)The hybrid synchronization of the driving-response fractional order complex network is described in detail.Complex network containing a large number of interacting nodes,the topology of network directly affects the inner synchronization of a complex network,the outer synchronization between two different complex networks depends more on the controller in the system.This thesis gives the sufficient conditions for the hybrid synchronization of two coupled fractional order complex networks by using the fractional-order nonlinear stability theory,Lyapunov stability theory and LaSalle invariance principle.Finally,the numerical simulations of fractional order hyperchaotic Lorenz,chaotic Lorenz and hyperchaotic Chen system are used to verify the correctness of the theoretical results.(3)The projective synchronization problem of two coupled fractional order complex networks is analyzed.According to the definition of projective synchronization,the fractional order controller is designed based on the fractional-order nonlinear stability theory and the adaptive control technique.The projective synchronization of the driving-response networks with the controller is realized.Finally,the effect of the projective synchronization control is verified by the numerical simulations of fractional order chaotic Lorenz,fractional order chaotic Liu and fractional order chaotic Chen system.