Quasi-synchronization Analyses Of Fractional-order Complex Dynamic Network

This paper mainly studies the quasi-synchronization of several kinds of fractional-order complex dynamic networks: quasi-synchronization of conformable fractional-order complex dynamic network,quasi-synchronization of fractional-order complex dynamic network with time delay and quasi-synchronization of non-autonomous fractional-order complex dynamic network with time delay and impulses.This paper is divided into five chapters.The first chapter is the introduction,which briefly describes the research background and significance of this paper and summarizes the main research content.In chapter 2,quasi-synchronization of conformable fractional-order complex dynamic networks is studied.Firstly,the fractional-order error dynamic system with periodic intermittent pinning controller was established.Then,by establishing some new conformable fractional differential inequalities,using Lyapunov function method and combining with the designed controller,sufficient conditions for quasi-synchronization of the complex dynamic network are obtained.Finally,a numerical example is given to verify the validity of the theoretical results.The third chapter mainly studies the quasi-synchronization of fractional-order complex dynamic networks with time delay.Firstly,the fractional delay error dynamic system with periodic intermittent pinning controller is established and the relevant preliminary knowledge is given.Then,by establishing some new nonlinear fractional delay differential inequalities and using Lyapunov function method and combining with the designed controller,the sufficient conditions for quasi-synchronization of the fractional-order complex dynamic network are obtained.Finally,a numerical example is given to verify the validity of the theoretical results.The fourth chapter mainly studies the quasi synchronization of non-autonomous fractional order complex dynamic networks with delay and impulse.Firstly,a non-autonomous fractional error dynamic system with time delay and impulse is established.Then,by establishing some new fractional differential inequalities and combining with the properties of the Mittag-Leffler function,the sufficient conditions for quasi-synchronization of the fractional order complex dynamic network are obtained.Finally,a numerical example is given to verify the validity of the theoretical results.The fifth chapter summarizes the work done in this paper,looks forward to the future research and puts forward some problems worth studying.