Nabil Rezaiki, Amel Boulfoul
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