Keyword: Kukles : Search

Advanced Search

SEARCH GUIDE

Results: 1 - 1of1

Follow results:

per page:

Sort: Relevance

Context for search term 1Search term 1*

All Dates

LastSelect static range

Custom Range

Select starting monthSelect starting year

Select ending monthSelect ending year

articleNo Access
Global Phase Portraits of Kukles Differential Systems with Homogeneous Polynomial Nonlinearities of Degree 6 Having a Center and Their Small Limit Cycles
- Jaume Llibre and
- Maurício Fronza da Silva
International Journal of Bifurcation and Chaos01 Mar 2016
Preview Abstract
We provide the nine topological global phase portraits in the Poincaré disk of the family of the centers of Kukles polynomial differential systems of the form $ẋ = - y,$ $ẋ = - y,$ $ẏ = x + a x^{5} y + b x^{3} y^{3} + c x y^{5},$ $ẏ = x + a x^{5} y + b x^{3} y^{3} + c x y^{5},$ where $x, y \in ℝ$ $x, y \in ℝ$ and $a, b, c$ $a, b, c$ are real parameters satisfying $a^{2} + b^{2} + c^{2} \neq 0 .$ $a^{2} + b^{2} + c^{2} \neq 0 .$ Using averaging theory up to sixth order we determine the number of limit cycles which bifurcate from the origin when we perturb this system first inside the class of all homogeneous polynomial differential systems of degree $6,$ $6,$ and second inside the class of all polynomial differential systems of degree $6 .$ $6 .$

1