Article
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Phase portraits of a class of Liénard equations
Version 1
: Received: 23 May 2024 / Approved: 24 May 2024 / Online: 24 May 2024 (09:42:01 CEST)
How to cite: Cheurfa, R.; Llibre, J.; Bendjeddou, A. Phase portraits of a class of Liénard equations. Preprints 2024, 2024051626. https://doi.org/10.20944/preprints202405.1626.v1 Cheurfa, R.; Llibre, J.; Bendjeddou, A. Phase portraits of a class of Liénard equations. Preprints 2024, 2024051626. https://doi.org/10.20944/preprints202405.1626.v1
Abstract
Recently several papers have been published on the Liénard equation
x'' +L x+m x^3+n x^5=0,
where the authors studied their explicit solutions and their applications. Here we describe the complete dynamics of these differential equations in the Poincar\'e disc. The Poincar\'e disc is the closed disc centered at the origin of coordinates of radius one, the whole plane R^2 is identified with the interior of this disc, and its boundary, the circle $\sss^1$ is identified with the infinity of R^2.
Keywords
Liénard equation; Poincaré disc; phase portraits
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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