| In the recent two decades, the research of synchronization and control of chaotic system attracts more attention and interest among people, and it shows wonderful achievements in many fields, relevant content are given in this thesis in brief. Firstly, it introduces the characters of chaos and the means to identify chaotic system, then some methods about synchronization and control of chaos are introduced, basing on some of the methods, this thesis proposes some new improved methods to study the 4D oscillator hyperchaotic system on synchronization and control, and it gets wonderful results.The 4D oscillator circuit is simple and easy to realize in reality, which shows complicated dynamic character, and it is a hyperchaotic system, it will show great value to study and research the synchronization and control of this hyperchaotic system. For this model, this thesis shows my works in the following parts:(1 ) It uses a gain function Kc (t) to equal the disadvantages effect of a common signal channel on the transmitted signal , considering the fact that signal may become distorted when it transform from one place to another place, the chaotic signal x1 and a standard direct current signal S(r) aresent through the same common signal channel, which become the distorted signal Kc(t)xi(t) and Kc(t)s(t), it can restore the real signal by using a self-adaptive compensator equipped at the front part of the receiving system, the gain of compensator is Kr , basing on the literature[115-116], this thesis gets news K r and it can be showed as the following equation:the value can be get from the following equation : The numerical simulation result shows :it can restore the distorted signal with the gain Kr proposed in this paper.(2) Using the method of parameter identification in literature [117-118], selecting gain function:giving the initial value of the parameter observer from the time serial of output variables of the system, the numerical simulation result shows that the parameter observer proposed in this paper can identify the unknown parameters of the system quickly and exactly no matter if the parameters keep invariable or change in some rule, and the identifying speed is faster than the method in [117-118], when the unknown parameters are being identified ,\vith parameter compensator, it can synchronizes two hyperchaotic systems completely even if some parameters mismatch.( 3 ) Basing on the stability theory, constructing the following Lyapunov function.it gets the controller with the same method, it can get therelevant controllers when parameters mismatch. The numerical simulation result shows that the controller proposed in this paper can synchronize two hyperchaotic system completely.( 4 ) Basing on the result [82 , 104] , which synchronization can be reached by using occasional driving or feedback filter, the following controllers are proposed in this thesis to synchronize two 4D oscillator hyperchaotic systems.The numerical results show that it can synchronize two hyperchaotic systems completely no matter if the parameters match or not.(5) Using the method APD ,it select a new drive signal S =x1- cx3 to synchronize the response system, the theory analysis and numerical simulation results show that it can synchronize two hyperchaotic systems completely with the drive signal S =x1- cx3, comparing with themethod of selecting signal in literature [114] , with the drive signal S =x1- cx3 , it can shortens the transient period of synchronization(6) Using the outside standard signal to control 4D oscillator hyperchaotic system, Basing on the stability theory, constructing the following Lyapunov function it gets the controller as following:The theory analysis and numerical simulation result show: using the controller above ,it can control the system to reach any desired stable point and period orbit. Basing on the stability theory, selecting controller as following:The theory analysis and numerical simulation result s...
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