A weakened Markus-Yamabe condition for planar polynomial differential systems of degree
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemática)

Date:	2023
Abstract:	For a general autonomous planar polynomial differential system, it is difficult to find conditions that are easy to verify and which guarantee global asymptotic stability, weakening the Markus-Yamabe condition. In this paper, we provide three conditions that guarantee the global asymptotic stability for polynomial differential systems of the form, where f1 has degree one, f2 has degree and has degree one in the variable y. As a consequence, we provide sufficient conditions, weaker than the Markus-Yamabe conditions that guarantee the global asymptotic stability for any generalized Liénard polynomial differential system of the form, with g1 and g2 polynomials of degrees n and m, respectively.
Grants:	European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2022/SGR-00113 Agencia Estatal de Investigación PID2019-104658GB-I00
Note:	Altres ajuts: acords transformatius de la UAB
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Global asymptotic stability ; Markus-Yamabe conjecture ; Planar polynomial vector fields
Published in:	Proceedings of the Edinburgh Mathematical Society, Vol. 66, Issue 4 (November 2023) , p. 1110-1118, ISSN 1464-3839

DOI: 10.1017/S0013091523000615

9 p, 384.7 KB

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