TY - JOUR
ID - 5760
TI - On the maximum number of limit cycles of a planar differential system
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Karfes, Sana
AU - Hadidi, Elbahi
AU - Kerker, Mohamed Amine
AD - Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria
Y1 - 2022
PY - 2022
VL - 13
IS - 1
SP - 1462
EP - 1478
KW - Periodic solution
KW - averaging method
KW - differential system
DO - 10.22075/ijnaa.2021.23049.2468
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_5760.html
L1 - https://ijnaa.semnan.ac.ir/article_5760_8a9b3bf64826dfec536fc0f11d6a15d0.pdf
ER -