Two Kinds Of Parameters Of Uncertain Chaotic Systems Synchronization And The Synchronization

As main one of the branches of nonlinear science, Chaos hasbecame a hot topic of research. For making benefit maximizationanalysis and forecast of behavior of chaotic systems,we must find waysto control chaotic systems. In1990, Pecora and Carroll found a kind ofchaotic synchronization method, many scholars do research tosynchronization of chaotic systems, adaptive synchronization is one ofthe typical method to achieve synchronization. In real life, manyparameters of chaotic systems are unknown, it is necessary to findmethods to achieve synchronization of chaotic systems with unknownparameters. Therefore, by using theory and numerical simulation, thispaper discussed synchronization of chaotic systems with unknownparameters. The main contribution of this paper is as follows,First, this paper introduces the theoretical study of Chaos, and thesignificance of study of chaos.In the second, two definitions of chaos is given, and simplyintroduced the Chaos control and chaos synchronization.At the same time, it presents three kinds of method forsynchronization of chaotic systems, such as adaptive synchronization,feedback synchronization and activate synchronization. MeanwhileLyapunov stability theory is introduced.In the third part, the synchronization of chaotic systems withunknown parameters is achieved by using adaptive control. Based onLyapunov stability theory, proper anti-synchronization controller and theparameters update rules are designed. The drive system and theresponse system can complete synchronization. Take Chen system asan example, the sufficient conditions can be obtained so that theanti-synchronization of Chen system with unknown parameters canachieve. At last, numerical simulation proved the effectiveness of the proposed method.The forth part is based on synchronous theory, time-delay chaoticsystem with unknown parameters is introduced. Based on Lyapunovstability theory and adaptive technology, it proved that designedsynchronous controller can make response system and drive systemachieve synchronization in theory. At the end, there takesgeneral chaotic systems in three dimensions as an example, numericalsimulation and proves that the method is effective.Finally, conclusions are drawn, the shortage and future works arepropesd.