延迟反馈引导混沌系统到周期解

Directing chaotic dynamics towards periodic motion by time-control

利用 Melnikov方法严格分析了延迟反馈实现引导混沌系统到周期解的控制机理 ,揭示出延迟时间与控制混沌的关系 ,得到一些新的结论 :延迟反馈实际上是一作用明显的扰动项 ,使得系统的稳定流形和不稳定流形不再横截相交 ;延迟时间关系到扰动量的大小 ,但不必是吸引子中不稳定周期轨道的周期整数倍。次谐轨道的

Melnikov′s method is used to analyze the mechanism of time delayed feedback control for chaotic motion in a typical perturbed planar Hamiltonian system. It is shown that the perturbation term yieldedbytime delayedfeedback control makes the stable manifolds and the unstable manifolds not intersect. The delayed time may not be an integer multiple of the period of the inherent unstable orbit in the chaotic attractor. Further Melnikov′s analyses examine the existence of low periodic subharmonic orbits in the controlled system.