Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory

作者：Benterki Rebiha; Llibre Jaurne^*

来源：Journal of Computational and Applied Mathematics, 2017, 313: 273-283.

DOI：10.1016/j.cam.2016.08.047

• Center
• Limit cycle
• Averaging method
• Phase portrait
• Generalized Kukles system

In this paper we classify the phase portraits in the Poincare disc of the centers of the generalized class of Kukles systems
(x) over dot = -y, (y) over dot = x + ax(3)y + bxy(3),
symmetric with respect to they-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4.

• 出版日期2017-3-15