Nabil Rezaiki, Amel Boulfoul

On the Limit Cycles that Can Bifurcate from a Uniform Isochronous Center via Averaging Method

abstract:
The aim of this paper is to determine an upper bound of number of limit cycles that can bifurcate from a uniform isochronous center of a cubic homogeneous planar polynomial differential system when we perturb it inside the class of all quintic polynomial differential systems. We prove that at most 5 limit cycles can bifurcate from the period annulus by using the averaging theory of first order and at most 19 limit cycles by applying the second order averaging method. This study needs many calculations that have been verified by Maple and Mathematica.

Mathematics Subject Classification: 34C07, 34G15, 34C05

Key words and phrases: Isochronous center, limit cycle, averaging theory, polynomial differential systems