On the maximum number of limit cycles of a planar differential system

	On the maximum number of limit cycles of a planar differential system
International Journal of Nonlinear Analysis and Applications
مقاله 121، دوره 13، شماره 1، خرداد 2022، صفحه 1462-1478 اصل مقاله (581.51 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23049.2468
نویسندگان
Sana Karfes؛ Elbahi Hadidi^* ؛ Mohamed Amine Kerker
Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria
چکیده
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.
کلیدواژه‌ها
Periodic solution؛ averaging method؛ differential system
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