一种控制蔡电路的分岔和混沌的方法

A METHOD TO CONTROL CHAOS AND BIFURCATION OF CHUA CIRCUIT

提出了用系统单变量的比例微分反馈实现蔡电路的分岔和混沌控制的方法.首先根据理论分析求出使蔡电路中不动点稳定的k1的取值范围和使系统发生Hopf分岔的临界值k0,然后对受控的系统做出了以k1(k1>k0)为控制参量的系统分岔图.由分岔图可以得到将系统控制到各种nP周期轨道的k1的取值范围,在这些范围内适当选择k1值,可以将蔡电路控制到1p,2p,3p,4p,6p和8p等周期轨道.数值仿真结果验证了这种控制分岔和混沌方法而且证明了理论结果的正确性.

In this paper,a method to control chaos and bifurcation of Chua circuit is proposed in which a single variable proportion and differential feedback is appropriately used.At first,theoretical analysis presents the range of value k1 to stabilize the unstable fixed points in Chau circuit and the critical value k0 to generate Hopf bifurcation.Then,the bifurcation diagram is plotted for the controlled system with k1(k1>k0) as bifurcation parameter.The range of value k1 to stabilize a certain nP periodic orbit in Chua circuit can be obtained through the bifurcation diagram.The periodic orbits such as 1p,2p,3p,4p,6p,8p can be stabilized with appropriate k1.Numerical simulation validates this method and demonstrates the correctness of theoretical analysis.