%0 Journal Article
%T On the maximum number of limit cycles of a planar differential system
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Karfes, Sana
%A Hadidi, Elbahi
%A Kerker, Mohamed Amine
%D 2022
%\ 03/01/2022
%V 13
%N 1
%P 1462-1478
%! On the maximum number of limit cycles of a planar differential system
%K Periodic solution
%K averaging method
%K differential system
%R 10.22075/ijnaa.2021.23049.2468
%X 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.
%U https://ijnaa.semnan.ac.ir/article_5760_8a9b3bf64826dfec536fc0f11d6a15d0.pdf