Bifurcation of limit cycles in quadratic Hamiltonian systems with various degree polynomial perturbations

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• 作者：P. Yu^a ; ^b ; ^{pyu@pyu1.apmaths.uwo.ca} ; M. Han^a
• 刊名：Chaos ; Solitons and Fractals
• 出版年：2012
• 期刊代码：5_09600779
• 类别：ph
• 出版时间：June, 2012
• 卷：45
• 期：6
• 页码：772-794
• 文件大小：371 K

摘要

In this paper, we consider bifurcation of limit cycles in planar quadratic Hamiltonian systems with various degree polynomial perturbations. Attention is focused on the limit cycles which may appear in the vicinity of an isolated center, and up to 20th-degree polynomial perturbations are investigated. Restricted to the first-order Melnikov function, the method of focus value computation is used to determine the maximal number, H₂(n), of small-amplitude limit cycles which may exist in the neighborhood of such a center. Besides the existing results H₂(2) = 2 and H₂(3) = 5, we shall show that for n = 3, 4, 鈥?#xA0;, 20.