Characteristic of the frequency and its applications in nonlinear autonomous systems
非线性自治系统频率特性及其利用

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.