Linping Peng, Zhaosheng Feng
Abstract:
This article concerns the bifurcation of limit cycles for a quartic
system with an isochronous center. By using the averaging theory,
it shows that under any small quartic homogeneous perturbations,
at most two limit cycles bifurcate from the period annulus of the
considered system, and this upper bound can be reached.
In addition, we study a family of perturbed isochronous systems
and prove that there are at most three limit cycles
bifurcating from the period annulus of the unperturbed one, and the
upper bound is sharp.
Submitted December 2, 2013. Published April 10, 2014.
Math Subject Classifications: 34C07, 37G15, 34C05.
Key Words: Bifurcation; limit cycles; homogeneous perturbation;
averaging method; isochronous center; period annulus.
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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, fax (86-10) 8231-7933 |
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Zhaosheng Feng Department of Mathematics University of Texas-Pan American Edinburg, Texas 78539, USA email: zsfeng@utpa.edu |
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