Electron. J. Diff. Equ., Vol. 2015 (2015), No. 111, pp. 1-27.

Limit cycles from a cubic reversible system via the third-order averaging method

Linping Peng, Zhaosheng Feng

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
Zhaosheng Feng
Department of Mathematics
University of Texas-Pan American
Edinburg, TX 78539, USA
email: zsfeng@utpa.edu

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