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.
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.
出处
《动力学与控制学报》
2012年第3期202-208,共7页
Journal of Dynamics and Control
基金
国家自然科学基金重点资助项目(11032009)
国家杰出青年科学基金资助项目(10825207)~~
