Research On Synchronization Of Fractional-Order Complex-Valued Complex Networks

Because of the strong applicability of complex networks,it has been widely used to depict physical models in the domains of natural sciences and engineering technology.The analysis of the topology and dynamic behavior of complex networks has become one of the current research hotspots.Compared with the integer-order model,the fractional-order complex network model can more accurately describe the changes in the memory and historical characteristics of real systems.Therefore,it is far-reaching significance to establish a dynamic model of fractional-order complex networks and study complex networks under the fractional-order idea.In particular,complex networks with complex-valued variables have a wider range of practical applications than real-valued complex networks.Fractional-order complex-valued complex networks deserve more in-depth research.Based on the fractional-order Lyapunov function method and related fractional-order techniques,this thesis studies the synchronization of several types of fractional-order complex-valued complex networks,including a class of fractional-order uncertain complex-valued networks with coupled delays,and a class of fractional-order uncertain complex-valued networks with time-varying coupling,and a class of fractional-order complex-valued neural networks based on memristors.The specific work of the full text is as follows:(1)Considering the delay and uncertainty existing in the actual system,the adaptive synchronization of fractional-order complex-valued complex networks with random parameters and coupled delays is studied.By designing an appropriate adaptive controller,with the help of fractional derivative inequalities and linear delay fractional order equations,sufficient conditions are obtained to ensure complete synchronization of the network.The synchronization conditions obtained can be applied to most complex network systems,with or without delay.(2)Aiming at the complex projection synchronization problem of fractional-order complex-valued dynamic networks,considering time-varying coupling and unknown parameters,based on adaptive control strategies,several adaptive controllers are designed to adjust the coupling strength and controller feedback gain to study the complex projectionsynchronization problem of the system.By constructing appropriate Lyapunov functions,some effective criteria are obtained to ensure that complex-valued dynamic networks achieve complex projection synchronization.In addition,based on the designed recognition law,unknown parameters in the network can be estimated.(3)The complex projection synchronization problem of fractional-order complex-valued memristive neural networks with multiple delays is discussed.In the framework of set-valued mapping and differential inclusion theory,a hybrid control strategy is designed to analyze the complex projection synchronization problem of the system.In addition,based on the stability theorem and comparison principle of fractional order systems with multiple time delays,some criteria are obtained to ensure the synchronization of the drive response network.