Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems
Li, Jie (Southwest Petroleum University. School of Sciences)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2025
Abstract:	The phase portraits of the planar linear differential systems are very well known. This is not the case for the phase portraits of the planar continuous piecewise linear differential systems. In this paper we classify the phase portraits of the class of planar continuous piecewise linear differential systems of the form x˙=a|x|+by+c,y˙=α|x|+βy+γ, in the Poincaré disc when aβ- bα≠ 0, and prove the existence and uniqueness of limit cycles. Note that on the straight line x= 0 these differential systems are only continuous.
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:	Continuous piecewise linear differential system ; Phase portrait ; Limit cycle ; Poincaré disc
Published in:	Differential Equations and Dynamical Systems, Vol. 33, Issue 2 (April 2025) , p. 689-746, ISSN 0974-6870

DOI: 10.1007/s12591-023-00666-7
PMID: 40271010

58 p, 6.6 MB

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