Bifurcation of limit cycles in quadratic Hamiltonian systems with various degree polynomial perturbations
نویسنده
چکیده
Article history: Received 1 May 2011 Accepted 15 February 2012 Available online 16 March 2012 0960-0779/$ see front matter 2012 Elsevier Ltd doi:10.1016/j.chaos.2012.02.010 ⇑ Corresponding author at: Department of Applied E-mail address: [email protected] (P. Y 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 H2ðnÞ 1⁄4 3 ðnþ 1Þ for n = 3,4, . . . ,20. 2012 Elsevier Ltd. All rights reserved.
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