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

Document Type : Research Paper

Authors

Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria

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

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###### Volume 13, Issue 1March 2022Pages 1462-1478
• Receive Date: 04 April 2021
• Accept Date: 12 September 2021