@article {
author = {Karfes, Sana and Hadidi, Elbahi and Kerker, Mohamed Amine},
title = {On the maximum number of limit cycles of a planar differential system},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {13},
number = {1},
pages = {1462-1478},
year = {2022},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2021.23049.2468},
abstract = {In this work, we are interested in the study of the limit cycles of a perturbed differential system in \(\mathbb{R}^2\), given as follows\[\left\{\begin{array}{l}\dot{x}=y, \\\dot{y}=-x-\varepsilon (1+\sin ^{m}(\theta ))\psi (x,y),%\end{array}%\right.\]where \(\varepsilon\) is small enough, \(m\) is a non-negative integer, \(\tan (\theta )=y/x\), and \(\psi (x,y)\) is a real polynomial of degree \(n\geq1\). We use the averaging theory of first-order to provide an upper bound for the maximum number of limit cycles. In the end, we present some numerical examples to illustrate the theoretical results.},
keywords = {Periodic solution,averaging method,differential system},
url = {https://ijnaa.semnan.ac.ir/article_5760.html},
eprint = {https://ijnaa.semnan.ac.ir/article_5760_8a9b3bf64826dfec536fc0f11d6a15d0.pdf}
}