一个新自治混沌系统及其混沌控制

In this paper, a new three-dimensional autonomous chaotic system is presented. Some of its basic dynamical properties are studied, such as the chaotic attractor, the feature of equilibrium points, Lyapunov exponents and fractal dimension. When the parameters are unknown, based on the Lyapunov theory, corresponding controller and the adaptive law of parameters are designed to suppress chaos to any unstable equilibrium by the adaptive control strategy. The asymptotical stability of chaos control is guaranteed in theory by lemma of Barbalat. Numerical simulations by Matlab are provided to demonstrate the validity of the proposed nonlinear controller and the adaptive law of parameters for controlling chaos.