Synchronization Of Fractional-order Dynamic Networks With Time-delay Coupling

In recent years,with the rapid development of information technology,the network plays an increasingly important role in the national economy and people's livelihood.Syn-chronous control,as the most basic and important research issue in network research,has received extensive attention.Since fractional calculus can better describe the memory and hereditary properties for variables of complex system,at the same time,the inevitability of time delays stimulates the scholars to study the synchronization of fractional-order dy-namic networks with time-delay coupling.Because the Caputo fractional derivative does not satisfy the composition properties of the operators,it is difficult for us to construct a suitable Lyapunov function to deal with time-delay terms and obtain practical algebraic criteria.Therefore,the study of the synchronization problem of fractional-order dynamic networks with time-delay coupling has wide application value.Based on the above inspi-ration,in this paper,the global synchronization and adaptive synchronization problems for fractional-order dynamic networks with time-delay coupling are discussed by using fractional Razumikhin method,the criterion of network synchronization is obtained.The main contents of this article are arranged as follows:In chapter 2,the global synchronization problem of fractional-order dynamic networks with discrete time-delay and distributed delay coupling is studied.By using fractional Razumikhin method and matrix inequalities,the criteria of three globally synchronized linear matrix inequalities for fractional-order dynamical networks with time-delay coupling are obtained.Finally,the validity of the theoretical results is verified by two examples and numerical simulations.In chapter 3,the adaptive synchronization problem for fractional dynamic networks with non-delay and time-delay coupling is studied.Based on the fractional Razumikhin method,and by designing a simple adaptive controller,two adaptive synchronization crite-ria for fractional-order dynamic networks with time-delay coupling are obtained.Finally,the validity of the theoret,ical results is verified by two examples and numerical simulations.The innovations of this paper have the following two aspects:First,the innovation of research methods.In this paper,the fractional-order Razumikhin method is used to study the synchronization problem of Caputo fractional dynamic network with time-delay coupling.Second,the research object innovation.In chapter 2,the global synchroniza-tion of fractional-order systems with distributed time-delay coupling is studied,and the criterion of network synchronization is obtained.