Linping Peng, Zhaosheng Feng
Abstract:
This article concerns the bifurcation of limit cycles from a cubic
integrable and non-Hamiltonian system. By using the averaging theory
of the first and second orders, we show that under any small cubic
homogeneous perturbation, at most two limit cycles bifurcate from
the period annulus of the unperturbed system, and this upper
bound is sharp. By using the averaging theory of the third order, we
show that two is also the maximal number of limit cycles emerging
from the period annulus of the unperturbed system.
Submitted January 12, 2015. Published April 22, 2015.
Math Subject Classifications: 34C07, 37G15, 34C05.
Key Words: Bifurcation; limit cycles;homogeneous perturbation;
averaging method; cubic 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 Fax 86-(10)8231-7933 email: penglp@buaa.edu.cn |
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Zhaosheng Feng Department of Mathematics University of Texas-Pan American Edinburg, TX 78539, USA email: zsfeng@utpa.edu |
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