On the maximum number of limit cycles of a planar differential system
نویسندگان
1 Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria
2 Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria
3 Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria
doi
10.22075/ijnaa.2021.23049.2468چکیده
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.
