混沌系统的递次错位反馈控制方法研究

设计了一种递次错位反馈控制（SDF）方法来实现混沌控制.介绍了SDF方法的控制原理,以单模激光Lorenz混沌系统作为典型的例子,验证了这种控制方法的有效性.比较单模激光Lorenz混沌系统受控前后相图、功率谱和相空间重构等刻划混沌系统的特征量.数值模拟结果显示, 受控系统的相图和相空间重构中由具有无穷嵌套自相似结构并限定在有限相空间内的混沌吸引子转变为周期数为2ⁿ×3^mp(n、m为整数)的周期轨道；同时,功率谱也由连续谱转变为具有独立单峰的分立谱.

The Study on Successive Dislocation Feedback Method of Chaos System

The successive dislocation feedback(SDF)method is proposed to control chaos system.Controlling principle is introduced,and single-mode laser Lorenz system is taken as a typical example to demonstrate the effectiveness of this method.The characteristic quantity of the nucontrolled and controlled system(phase figure、power spectrums、reconstruction of phase space etc.) is compared with each ather.The numerical simulation results show that the phase figure and reconstruction of phase space in the system can be changed into the periodic states from the chaotic attractor which has self similar structure of infinite embedment and is restricted within terminate phase space,and the periodic numbers of different periodic orbits are 2~n×3~mp(n,m are integers);meanwhile the power spectrums of the system can also be changed from the continuous spectrum into the discrete spectrums with some separation single peaks.