伪振子分析法的证明及其在高阶Hopf分岔中的应用
俞亚娟，王在华
摘要:采用由闭轨分岔出极限环的思路给出了伪振子分析法的严格证明,所得结果推广了伪振子分析法的主要结论,使其能够应用于高阶Hopf分岔问题,其中分岔周期解的稳定性分析需要高于三次的非线性项.论文给出两个数值算例检验了伪振子分析法的有效性.
关键词：伪振子分析法；Hopf 分岔；时滞微分方程；极限环
Proof of the pseudo-oscillator analysis and its application in high-order hopf bifurcation
Yajuan Yu, Zaihua Wang
Abstract：Based on the idea of bifurcating a limit cycle from a closed orbit of a nonlinear system, this paper presents a mathematical proof of the pseudo-oscillator analysis developed recently. The result generalizes the main conclusions of the pseudo-oscillator analysis, and it can also be used to study the problem of high-order Hopf bifurcation, whose stability requires nonlinear terms with order larger than 3. Two illustrative examples are given for demonstration.
Keyword：pseudo-oscillator analysis; Hopf bifurcation; time-delay; limit circle
原文链接：http://dlxykzxb.cnjournals.net/jdc/article/abstract/20120303?st=search
