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Bifurcation of Limit Cycles from a Quintic Center via the Second Order Averaging Method

School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, LIMB of the Ministry of Education, Beijing 100191, P. R. China

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and

Zhaosheng Feng

Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, USA

Author for correspondence.

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https://doi.org/10.1142/S0218127415500479Cited by:5 (Source: Crossref)

Abstract

This paper is concerned with the bifurcation of limit cycles from a quintic system with one center. By using the averaging theory, we show that under any small quintic homogeneous perturbations, up to order 1 in ε, at most three limit cycles bifurcate from periodic orbits of the considered system, and this upper bound can be reached. Up to order 2 in ε, at most seven limit cycles emerge from periodic orbits of the unperturbed one.

This work is supported by the National Science Foundation of China under Nos. 11371046 and 11290141.

Keywords:

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