On the limit cycles of polynomial vector field

By Jaume Llibre, Grzegorz Swirszcz. 2011

47 citations recorded by the source corpus.

In this paper we study the limit cycles which can bifurcate from the periodic orbits of the center located at the origin of the quadratic polynomial differential system ẋ = −y(1+x), ẏ = x(1+x), and of the cubic polynomial differential system ẋ = −y(1−x2−y2), ẏ = x(1− x2 − y2), when we perturb them in the class of all polynomial vector fields with quadratic and cubic homogenous nonlinearities, respectively. For doing this study we use the averaging theory.

View Paper: https://www.semanticscholar.org/paper/867429a190724d4052527aea757c9a040375d04e

Citations in the corpus

• Limit cycles for discontinuous quadratic differential systems with two zones (2014, methodology): “In order to study the number of zeros of the averaged function (7) we will use the following result proved in [14].”