Langford系统的混沌控制

Chaos Control in the Langford System

分析了Langford系统Hopf分叉和准周期分叉行为,给出了确定通向混沌运动的准周期分叉点的研究方法.利用该系统具有的对称性,设计非线性状态反馈控制律,得到周期解失稳时产生准周期运动的条件,推导出控制增益与分叉参数之间的解析关系式,给出参数控制曲线,从而间接地实现了对系统混沌运动的延迟抑制.通过对系统受控前后Lya-punov指数的数值计算和相轨迹的数值模拟,验证了理论上解析结果的正确性以及控制的有效性.

This paper investigated the characteristics of the Hopf and quasi-periodic bifurcations in the Langford system and proposed how to determine the value of the quasi-periodlc bifurcation which leads to the chaos. For this system to possess a high degree of symmetry, a nonlinear feedback control law was designed to delay the emerging of chaos indirectly. The conditions in which a quasi-periodic motion occurs were deduced. Meanwhile, the relationship between the bifurcation parameter and the control gain was obtained and a gain-parameter curve was drawn. For the uncontrolled and controlled systems, the numerical simulations along with the Lyapunov exponents agreed well with the analytic prediction and the control was achieved.