混沌Lorenz系统延迟反馈控制的机理分析

利用广义Hamilton系统理论的Melnikov方法,严格分析了延迟反馈方法控制混沌Lorenz系统到周期解的机理,揭示了延迟时间与控制混沌的关系.延迟反馈项实际上是一个作用明显的扰动项,通过选择合适的参数,使得系统的稳定流形与不稳定流形不再横截相交,Smale意义下的混沌受到抑制,将Lorenz混沌系统引导到各种不同的周期轨道;可见,延迟时间关系到控制扰动量的大小,但不必是混沌吸引子内嵌不稳定周期轨道的周期整数倍.另外,通过数值仿真,其结果与理论分析相符,从而表明了该分析方法的有效性.

Analyze the time-delayed feedback control of chaotic Lorenz system

The paper focuses on the problem of suppressing chaos in the time-delayed feedback control system. The validity of Melnikov' s method in the generalized Hamilton system perturbed by weak periodic terms and time-delay terms is discussed. The Malnikov' s technique is applied to analyze the mechanism of time-delayed feedback control for Lorenz systems. It is shown that the time-delayed feedback control in fact is a perturbation term, which with a suitable selection of parameters makes the stable manifolds no longer intersecting the unstable manifolds. Then it is revealed that the time delay can be independent of the period of the inherent unstable orbit in the chaotic attractor. Moreover, the numerical simulation results are presented to demonstrate the effectiveness of the theoretical analysis.