Limit cycles for planar differential systems with quasi-homogeneous nonlinearities
Abstract
In this paper we study the estimate for the limit cycles of the planar differential systems of (p,q)-quasi-homogeneous polynomials nonlinearities. We give a condition on the polynomials to let the system have at most two limit cycles by introducing a new form of transformation. The tool that we mainly use is generalized polar coordinates and a fact introduced by Gasull and Llibre in estimating the number of limit cycles. This is achieved by estimating the number of isolated periodic solutions of Abel equation.
Copyright © 2019 Khalil I.T. Al-Dosary. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
K. I. T. Al-Dosary, Limit cycles for planar differential systems with quasi-homogeneous nonlinearities, J. Math. Comput. Sci. 9 (2019), 365–371. https://doi.org/10.28919/jmcs/4035
BibTeX
@article{Al-Dosary2019,
author = {Al-Dosary, Khalil I.T.},
title = {Limit cycles for planar differential systems with quasi-homogeneous nonlinearities},
journal = {J. Math. Comput. Sci.},
volume = {9},
year = {2019},
pages = {365--371},
doi = {10.28919/jmcs/4035}
}