一类新自治混沌系统的非线性反馈控制

Nonlinear Feedback Control for a New Autonomous Chaotic System

通过数值方法,研究了一类新的自治混沌系统的非线性反馈控制问题.利用系统的Lyapunov指数和分数维以及在不同相平面上的Poincaré截面图等混沌判据对系统的高分数维混沌特性进行了分析.基于非线性延迟反馈控制法则,选取了相应的合理控制参数,对这一类含有多个非线性项的三维自治混沌系统进行了有效的控制.结合相图,说明了这种方法对高分数维混沌系统的有效性和适用性.

The problem of controlling a new chaotic system is investigated using numerical analysis. We analyze the property of chaotic attractor using some useful criterions, such as time history, Poincaré maps in different surfaces of section, Lyapunov exponents and Lyapunov dimension from time series et al. The controls parameters are selected based on the nonlinear feedback controlling method, which can effectively guide the chaotic trajectories of a new three-dimensional autonomous system with multi-nonlinearities to periodic orbits. Numerical simulations show the effectiveness and applicability of the method, which are shown in phase portraits.