Electronic Journal of Differential Equations,
Vol. 2015 (2015), No. 246, pp. 1-11.
Title: Limit cycles bifurcating from the period annulus of a uniform isochronous
center in a quartic polynomial differential system
Authors: Jackson Itikawa (Univ. Autonoma de Barcelona, Spain)
Jaume Llibre (Univ. Autonoma de Barcelona, Spain)
Abstract:
We study the number of limit cycles that bifurcate from the periodic
solutions surrounding a uniform isochronous center located at the
origin of the quartic polynomial differential system
$$
\dot{x}=-y+xy(x^2+y^2),\quad \dot{y}=x+y^2(x^2+y^2),
$$
when perturbed in the class of all quartic polynomial differential
systems. Using the averaging theory of first order we show that at
least 8 limit cycles bifurcate from the period annulus of the center.
Recently this problem was studied by Peng and Feng [9],
where the authors found 3 limit cycles.
Submitted October 15, 2014. Published September 22, 2015.
Math Subject Classifications: 34A36, 34C07, 34C25, 37G15.
Key Words: Polynomial vector field; limit cycle; averaging method;
periodic orbit; uniform isochronous center.