Study On Chaos Identification And Chaos Control

In 1963, the first chaos model was shown in the paper “Deterministic Non-periodic Flow” which was written by Lorenz. From then on, Chaos theory became a focus in the research field, and was combined with many subjects to produce more overlapping areas. Chaos is harmful in many cases, so chaos is made from theory to practical application with the help of chaos control. As a hot topic, the research of chaotic control has made a remarkable progress. Lyapunov exponent is one of the important characteristics of chaos, which is widely used in determining the existence of chaos.In this thesis, the new butterfly-chaotic and hyperchaotic systems are studied. With the help of Lyapunov exponent, the stability and chaotic characteristic are analysed. Then two following questions are mainly solved, and some results are given as follows :Firstly, the sliding mode control of a new butterfly-chaotic system is given. A new three-dimensional autonomous chaotic system is given and the states of chaotic attractor is shown intuitively in each plane. The chaotic characteristic is proved for the reason that the system has positive Lyapunov exponent. Some basic dynamical behaviors, such as the equilibrium, stability and dissipation are studied. On the basis of stability theory, a controller is designed. With the method of adaptive sliding mode control, the system finally reaches the stable state. Numerical simulations are applied to verify the effectiveness of the controllers.Secondly, this paper puts forward to a new hyperchaotic system. With the help of Lyapunov exponent, the system is confirmed to be a hyperchaotic system and feedback control method is applied to the hyperchaotic system. Based on a three-dimensional chaotic system, a new hyperchaotic system is constructed. Numerical simulation shows that there are at least two positive Lyapunov exponents in this system, and some basic dynamical behaviors are analysed to prove its obvious hyperchaotic characteristic. Two kinds of feedback control methods are promoted to the hyperchaos. Proper controller is found to suppress the hyperchaos to the unstable equilibrium. The effect of two control methods is compared, and the numerical simulation shows the methods are effective.