寻找动力学系统主分岔参数的一种方法

A method to find the main bifurcation parameter of dynamic system

对于多参数系统,为了能很好的研究系统动力学特性随参数的变化,给出了一种寻找动力学系统主分岔参数的方法.通过对特征根进行扰动,来判断对系统动力学特性影响最主要的参数.针对不同的特征根类型给出了不同的算法,并举例进行了验证.该方法能有效地从诸多的系统参数中识别出对系统动力学特性影响比较大的参数.而且按照参数对系统动力特性影响的大小进行排序,同样可识别出主要的开折参数.该方法不仅适用于自治系统,同样适用于非自治系统.

To study the change of bifurcation properties of the system with structural parameters,a method to find the main bifurcation parameter of the dynamic system is presented in this paper.After disturbing the eigenvalue of Frechet matrix,the main bifurcation parameter is found.Different algorithms are given for different eigenvalue forms.The bifurcation parameter which has appreciable effect on dynamic characteristics of the system can be effectively identified from multiple parameters.And the unfolding parameters can be identified as well according to the effects of parameters on the system.This method can not only be used in autonomous systems,but also in nonautonomous systems.