Synchronization Studies Of Several Complex Systems

This paper is based on theoretical construction of synchronization methods.Applications potential of various synchronization methods in reality were discussed indepth. Synchronization is a very common natural phenomenon, in the long course of itsevolution and development, which has been applied to many fields extensively.Synchronization plays a key role in our life. Therefore, how to improve and optimizesynchronization methods, how to build and select synchronization objects, how to apply themore advanced methods of synchronization to even more complex chaotic systems oremerging complex networks, have become a hot topic and have attracted wide attentionfrom many scholars. At the same time, with the development of synchronization, innercharacters of complex networks are widely recognized, which can help us can explain manycomplex phenomena in nature and realistic society. Therefore, synchronization study ofcomplex network has some practical significance and wider application prospects. Thispaper contrasted the respective merits of different synchronization methods in theillustration of different classificatory by some specific examples. Through rigoroustheoretical derivations and numerical simulations, those synchronization methods wereapplied to the spatiotemporal chaos and complex networks. The main content of this papercan be summarized as follows:Chapter one is an introduction. Fistly, the concept of chaotic synchronization andsignificance, a summary of complex networks, research status of complex networks werepresented. Then, main contents and innovative points of this paper were given. Theseintroduced basic concepts are the cornerstone of subsequent discussions.Chapter two investigates modified function projective lag synchronization ofspatiotemporal chaos with disturbances. A control scheme is designed via active slidingmode control. The states of two chaotic systems with disturbances are asymptotically lagsynchronized up to a desired scaling function matrix. The control law is applied tospatiotemporal Gray-Scott systems. Numerical simulations are presented to demonstrate theeffectiveness of the proposed active sliding mode controllers.Chapter three investigates modified function projective lag synchronization ofspatiotemporal chaos with uncertain parameters using adaptive method. A control scheme isdesigned via Lyapunov stability theory. The synchronization of spatiotemporal chaosbetween a drive system and a response system with time-delay is implemented by addingthe adaptive controllers. The adaptive control law and the parameter update law are appliedto two identical spatiotemporal Gray-Scott systems. Numerical results demonstrate thefeasibility and the effectiveness of the proposed approach.In chapter four, three control schemes are presented in synchronization ofspatiotemporal chaos in complex networks. The time-delay, the projection and the randomdisturbances are accounted in the synchronization. The control laws are designed via the active sliding mode control, the backstepping control and the master stability function. Themerits of each scheme are numerically demonstrated in synchronization of spatiotemporalGray-Scott systems.Chapter five initiates a novel approach for simultaneously identifying unknownparameters and synchronizing time-delayed complex community networks withnonidentical nodes. Based on the LaSalle’s invariance principle, a criterion is established byconstructing an effective control identification scheme and adjusting automatically theadaptive coupling strength. The proposed control law is applied to a complex communitynetwork which is periodically synchronized to a different chaotic trajectory. Numericalsimulations are presented to demonstrate the feasibility of the proposed methods.Chapter six initiates an approach for simultaneously synchronizing time-delayedcomplex community networks with nonidentical spatiotemporal nodes. Based on theLaSalle’s invariance principle, a criterion is established by adjusting automatically theadaptive coupling strength. The Fitzhugh–Nagumo and Panfilov as spatiotemporal nodesare applied to the synchronization of a complex community network. Numerical simulationsare presented to demonstrate the feasibility of the proposed methods.Chapter seven investigates cross projective synchronization of spatiotemporal andtime-varying chaos with disturbances. A control scheme is designed via active sliding modecontrol. The states of two chaotic systems with disturbances are asymptotically projectivesynchronized up to a desired scaling matrix. The control law is applied to spatiotemporaland time-varying systems. Numerical simulations are presented to demonstrate theeffectiveness of the cross projective synchronization between spatiotemporal andtime-varying chaos.Chapter8is the summary and forecasting.