| Fractional-order multiplex networks are the generalization of fractional-order com-plex networks.Its structure and form are more complex than complex networks.Com-plex networks can be regarded as a special case of multiplex networks.Complex net-works is widely used in Internet,scientific citation system,World Wide Webs and other fields.The application of multiplex networks are more extensive than that of complex networks.From the communication between countries to the communication between people,they can be abstracted into multiplex networks.Fractional-order multiplex net-works have the characteristics of heredity and memory,which make them more advan-tageous than multiplex networks.Therefore,this thesis studies the synchronization of fractional-order multiplex networks by some control means.The main contents are as follows:In the first chapter,the background knowledge and development of complex net-works,finite time synchronization,fractional-order and multiplex networks are intro-duced.In the second chapter,finite-time inter-layer projective synchronization(FIPS)of fractional-order two-layer networks(FTN)based on sliding mode control(SMC)tech-nique is investigated.Firstly,in order to realize the FIPS of FTN,a fractional-order integral sliding mode surface(SMS)is established.Then,through the theory of SMC,this chapter designs a sliding mode controller to ensure the appearance of sliding mod-e motion.According to the fractional Lyapunov direct method,the trajectories of the system are driven to the proposed SMS,and some novel sufficient conditions for FIPS of FTN are derived.Furthermore,as two special cases of FIPS,finite-time inter-layer synchronization and finite-time inter-layer anti-synchronization for the FTN are studied.Finally,this chapter takes the fractional-order chaotic Lu’s ystem and the fractional-order chaotic Chen’s system as the isolated node of the first layer system and the second layer system,respectively.And the numerical simulations are given to demonstrate the feasibility and validity of the proposed theoretical results.In the third chapter,the finite-time complete synchronization of fractional-order multiplex networks is investigated by using a hybrid feedback controller.Firstly,by uti-lizing fractional-order differential inequalities,some innovative sufficient conditions are derived to guarantee complete synchronization for fractional-order multiplex networks in a finite time.The settling time obtained in most articles is independent of the order of fractional-order,however,this chapter shows an explicit expression for the settling time in the multiplex networks,which can reveal the relationship between the settling time and the order of fractional-order.Moreover,the issue of finite-time complete synchro-nization for fractional-order multiplex networks when there are no inter-layer couplings or intra-layer couplings is considered,and it is found that the inter-layer couplings and the intra-layer couplings have great influence on the network synchronization region.Fi-nally,the theoretical results which we derived are attested to be indeed feasible through numerical simulations.The fourth chapter summarizes the main work of this thesis and discusses the short-comings of the thesis and the direction of future research. |
