非线性自治系统频率特性及其利用

Characteristic of the frequency and its applications in nonlinear autonomous systems

用数值模拟方法对三维非线性混沌系统进行了分析 ,发现衰减项参量的变化基本不影响系统的周期 (指在同一周期内 ) ,并且系统基频与分频 (基本周期与倍周期 )之间还存在着近似的简单倍数关系 .另外 ,还将Hopf分支理论中的实用分析方法应用到某些系统 ,解析地确定出系统开始出现稳定周期解 (分岔 )的临界位置、基本周期的近似值及分岔方向等有关特征量 .进一步利用确定系统基本周期的方法以及基本周期和其他周期关系的规律 。

Some three dimensional nonlinear chaotic systems have been investigated numerically. It is found that the periods in the systems almost do not drift with the variety of damping parameters (within the same period) and a simple approximate relationship exists between the foundational period and the other periods. In addition, the practical method of the theory of Hopf bifurcation is applied to some systems. As the result, we analytically confirmed some essential systemic parameters, such as the critical point at which the stable periodical solutions appear, the approximation of the foundational period and the direction of Hopf bifurcation etc. Using the method and the result stated above, we also analyze two chaotic systems that can be successfully controlled by the method of time delayed feedback.