2021 On a class of polynomial differential systems of degree 4: phase portraits and limit cycles
Jaume Llibre, Tayeb Salhi
Topol. Methods Nonlinear Anal. 57(2): 441-463 (2021). DOI: 10.12775/TMNA.2020.042

Abstract

In this paper we characterize the phase portraits in the Poincaré disc of the class of polynomial differential systems of the form \begin{equation*} \dot{x}=-y,\qquad \dot{y} =x+ax^{4}+bx^{2}y^{2}+cy^{4}, \end{equation*} with $a^2+b^2+c^2\neq0$, which are symmetric with respect to the $x$-axis. Such systems have a center at the origin of coordinates. Moreover, using the averaging theory of five order, we study the number of limit cycles which can bifurcate from the period annulus of this center when it is perturbed inside the class of all polynomial differential systems of degree $4$.

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Jaume Llibre. Tayeb Salhi. "On a class of polynomial differential systems of degree 4: phase portraits and limit cycles." Topol. Methods Nonlinear Anal. 57 (2) 441 - 463, 2021. https://doi.org/10.12775/TMNA.2020.042

Information

Published: 2021
First available in Project Euclid: 4 August 2021

MathSciNet: MR4359721
zbMATH: 1486.34072
Digital Object Identifier: 10.12775/TMNA.2020.042

Keywords: centers , limit cycles , phase portraits , Polynomial differential systems , polynomial vector fields

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.57 • No. 2 • 2021
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