利用间歇非线性时滞反馈控制一维Logistic系统的混沌运动

The Chaotic Control of Logistic Map Based on the Occasional Nonlinear Time-delayed Feedback

提出用间歇非线性时滞反馈控制混沌的方法利用分岔图和Lyapunov指数等数值分析方法,研究发现形式为u（Xn,Xn-k）=c·Xn·Xn-k的非线性时滞反馈,可以对一维Logistic系统的混沌进行有效的控制,只要选定合适的反馈系数C、时滞参数k和问歇反馈周期N,就可以将系统从混沌状态控制到稳定的周期状态,而且被控系统的稳态周期数是选定的间歇反馈周期N的整数倍.

This paper raises the method which uses the occasional nonlinear time-delayed feedback to control chaos. By using the numerical analysis methods of bifurcation diagram and Lyapunov exponent, it discovers the nonlinear time-delayed feedback as the form of u(xn,xn-k) = c·xn·xn-k can control the systematic chaos effectively. As long the proper feedback coefficient c ,time-delayed coefficient k and occasional feedback period N is chosen, we not only can control the system from chaos to the steady periodic orbit, but also the steady period is the integral multiple of the occasional feedback period N.