Analyze the time-delayed feedback control of chaotic Lorenz system
混沌Lorenz系统延迟反馈控制的机理分析

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.