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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 | ||
| تاریخ دریافت: 15 فروردین 1400، تاریخ پذیرش: 21 شهریور 1400 | ||
| 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 | ||
| مراجع | ||
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