The Ultimate Bound For A Kind Of Chaotic Systems And Its Application In Chaos Synchronization

Chaos is one of the common phenomena in the nature. It reveals the complexconnection between nature and human social life. The study can make human being tounderstand the nature, improve the nature and get along harmoniously better with eachother. Chaos control and synchronization relates to all fields of the life of human. Theresearch into the control and synchronization of chaotic systems becomes widespreadand turns out to be a hot topic at present. It involved in every field of human social life.The study on ultimate bound of chaotic systems is helpful for the study of theasymptotic behavior of chaotic systems and the behavior of dynamical systems can berestricted to this set. The behavior of three-dimensional systems and four-dimensionalsystems has widely studied at present, but a five-dimensional system has been studiedscarce. This paper studies the control and synchronization of five-dimensionalna ve-stokes chaotic systems. This article consists of four parts as follow:Chapter1introduces the research background and the meanings of the chaoticsystem. Especially its results of the ultimate bound of some typical chaotic systems.Chapter2introduces the definition of chaos, chaos control and conception of chaossynchronization, and basic knowledge of stability theory of Lyapunov functiontheories.Chapter3, Firstly, to construct the positive definite function according to themathematical model which has been given, make the function of derivative is zerowhile it go along the system. According to the maximum positive definite functionmodel which is obtained, and a positive definite function corresponds to the spherecontaining the ellipse corresponding ellipsoid, and analyze the progressive behavior ofsolutions of the systems according to the spherical for interface, inference this ball to bethe end boundary of a system error estimate as defined by the ultimate bound. Secondly,the dissipation of the system was investigated in theory, the numerical simulation resultsshow that the system has the chaotic attractor, and further study the system balance,symmetry and the numerical simulation of expected near the equilibrium bifurcationphenomenon and the change of system parameters over time. Finally, construct alyapunov function, use the nonlinear feedback control method to set up a function withtwo control parameters of controller, make the original system to be a driving system,and adding the control system to be response of the system. According to the lyapunov asymptotic stability theory and the definition of complete synchronized, theoreticallyanalysis of the system is feasible in the synchronous control. Through numericalsimulation, it can meet the expectation of the theory and further illustrate this control iseffective.Finally, it summarizes this article’s research and looks forward into the future.