Electron. J. Diff. Equ., Vol. 2014 (2014), No. 95, pp. 1-14.

Bifurcation of limit cycles from quartic isochronous systems

Linping Peng, Zhaosheng Feng

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

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