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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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[1] S. Badi and A. Makhlouf, Limit cycles of the generalized Li´enard differential equation via averaging theory, Ann. Di. Eqs. 27(4) (2011) 472–479. [2] I.S. Berezin and N.P. Zhidkv, Computing Methods, vol. II, Pergamon Press, Oxford, 1964. [3] A. Buica, J. Gin´e and J. Llibre, Bifurcation of limit cycles from a polynomial degenerate center, Adv. Nonlinear Stud. 10 (2010) 597–609. [4] A. Buica and J. Llibre, Averaging methods for finding periodic orbits via Brouwer degree, Bull. Sci. Math. 128 (2004) 7 22. [5] T. Chen and J. Llibre, Limit cycles of a second-order differential equation, Appl. Math. Lett. 88 (2019) 111–117. [6] A. Cima, J. Llibre, and M. A Teixeira, Limit cycles of some polynomial differential system in dimension 2, 3 and 4 via averaging theory, Appl. Anal. 87 (2008) 149–164. [7] N. Hirano and S. Rybicki, Existence of limit cycles for coupled Van der Pol equations, J. Differ. Equ. 195(1) (2003) 194-209. [8] J. Llibre and A.C. Mereu, Limit cycles for generalized Kukles polynomial differential systems, Nonlinear Anal. 74 (2011) 1261–1271. [9] J. Llibre, R. Moeckel and C. Sim´o, Central Configurations, Periodic Orbits and Hamiltonian Systems, Advanced Courses in Mathematics CRM Barcelona, Birkh¨auser, 2015. [10] N. Mellahi, A. Boulfoul and A. Makhlouf, Maximum number of limit cycles for generalized Kukles polynomial differential systems, Differ. Equ. Dyn. Syst. 27 (2019) 493-–514. [11] L. Perko, Differential Equations and Dynamical Systems, Texts in Applied Mathematics, V. 7, 3rd edition.Springer, New York, 2000. [12] H. Poincar´e, M´emoire sur les courbes d´efinies par une ´equation diff´erentielle I, II, J. Math. Pures Appl. 7 (1881) 375–422; 8 (1882) 251–296. [13] E. S´aez and I. Szanto, Bifurcations of limit cycles in Kukles systems of arbitrary degree with invariant ellipse, Appl. Math. Lett. 25 (2012) 1695-–1700. [14] H. Shi, Y. Bai and M. Han, On the maximum number of limit cycles for a piecewise smooth differential system, Bull. Sci. Math. 163 (2020) 102887. [15] D. Zwillinger, Table of Integrals, Series and Products, 2014, ISBN: 978-0-12-384933-5. | ||
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