Linping Peng, Bo Huang
Abstract:
This article concerns the bifurcation of limit cycles from a quadratic
integrable and non-Hamiltonian system. By using the averaging theory,
we show that under any small quadratic homogeneous perturbation,
there is at most one limit cycle for the first order bifurcation
and two for the second-order bifurcation arising from the period annulus
of the unperturbed system, respectively. Moreover, in each case the upper
bound is sharp.
Submitted March 2, 2016. Published March 28, 2017.
Math Subject Classifications: 34C07, 37G15, 34C05.
Key Words: Hamiltonian system; bifurcation; limit cycles; perturbation;
averaging method; quadratic center.
Show me the PDF file (245 KB), TEX file for this article.
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Linping Peng School of Mathematics and System Sciences Beihang University LIMB of the Ministry of Education Beijing 100191, China email: penglp@buaa.edu.cn |
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Bo Huang School of Mathematics and System Sciences Beihang University LIMB of the Ministry of Education Beijing, 100191, China email: bohuang0407@buaa.edu.cn |
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