Studies Of Basic Dynamical Properties, Control And Synchronization Of A New Hyperchaos

Chaos is a kind of special type in the nonlinear dynamical system,it widely lies in nature.Recently,chaos control and synchronization have been an active research of the nonlinear subject.This new technology promises to have significant impact on many novel engineering applications.Compared to chaotic system,hyperchaotic system has much more complex dynamical behavior.Its randomness and indeterminacy has enhanced much,hence hyperchaos has much more extensive value in engineering applications.For example,more recent study indicates that, hyperchaotic signal is more difficult to predict by common methods, which are usually used for low dimension chaos signal.Therefore,it has great application significance to analyze hyperchaotic system with at least two positive Lyapunov exponents.Based on the research results of chaos and hyperchaos in theory,the thesis has mainly analyzed the properties of a new hyperchaotic system, and studied its control and synchronization.The main content is depicted as follows:Firstly,in first two chapters,control and synchronization of chaos and hyperchaos in the research background and study conditions are introduced,meanwhile,the definition,basic characteristic and analysis methods of chaotic and hyperhaotic systems are recommended.In the third chapter,based on a three-dimension chaotic system,a new four-dimension hyperchaotic system is constructed by the nonlinear feedback control method.Characteristic of this new hyperhaotic system is studied in detail,including validating the hyperchaotic system quality, analyzing phase track,calculating Lyapunov exponents,drawing bifurcation figure and so on.Simulation results indicate the dynamical behavior of this hyperhaotic system is very complex.Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium,periodic orbits and quasi-periodic orbits.The Matlab software is used to prove the effectiveness of this method.The forth chapter discusses projective synchronization of the new hyperchaotic system.The different nonlinear feedback controllers are designed by an active control method for synchronization of two chaotic systems with the same or different structures.The proposed technique allows us to arbitrarily direct the scaling factor to a desired value.In addition,the modified projective synchronization of the new hyperchaotic system with unknown parameters including the unknown coefficients of nonlinear terms is studied by using adaptive control.Numerical simulation is provided to show the effectiveness of the theoretical analysis.