用直线稳定方法控制耦合哈密顿系统的混沌运动

Controlling Chaos by Straight-line Stabilization Method in Two Coupled Standard Maps

讨论了不稳定不动点邻域的不稳定轨道的稳定问题.通过对系统施加外部的控制信号,将直线稳定方法推广到控制高维保守系统-耦合标准映象的混沌运动.通过对外加控制信号的调整,使系统不稳定不动点邻域的不稳定轨道沿着连接任意时刻轨道点和该不动点的直线趋向不动点,从而使难于控制的高维保守系统的不稳定轨道趋于稳定.这种方法不需要事先掌握系统动力行为,而且具有较强的抗干扰能力.

The stabilization of an unstable periodic orbit in a neighborhood of an unstable fixed point is studied. By adding the external control signal, the straight\|line stabilization method is applied to a high\|dimensional Hamiltonian system, that is,two coupled standard maps. The method can stabilize an unstable periodic orbit in a neighborhood of an unstable fixed point, so the difficult problem of the unstable periodic orbits for high\|dimensional Hamiltonian systems can be solved. The method does not require any previous knowledge of the system and is robust under the presence of weak external noise.