最小Lipschiz常数及其在稳定邻域估计中的应用

The Minimal Lipschiz Constant and Its Application to the Estimation of the Stable Basin

引入最小Lipschiz常数结合极坐标变换提出了一种新的估计最大吸引域半径的方法.并将该方法应用到混沌控制中的稳定邻域估计.以混沌的Henon和Ikeda映射动力系统为例,说明了所给算法的实施方法,并给出了相应的数值模拟以证明方法的有效性.

In this paper, we apply linear feedback control to discrete chaotic system, and based on minimal Lipschiz constant and polar transformation, give an algorithm for estimating the radius of this basin is bound to be exist for a nonlinear discrete system, whose goal dynamics is either periodic orbits or fixed point. Furthermore, we take the well-known Henon system and Ikeda system as examples to illustrate the implementation of our theory, and give the corresponding simulations to reinforce our method.