Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems

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 differentia...

Descripción completa

Detalles Bibliográficos
Autores: Li, Jie|||0000-0003-0134-7674, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:287940
Acceso en línea:https://ddd.uab.cat/record/287940
https://dx.doi.org/urn:doi:10.1007/s12591-023-00666-7
Access Level:acceso abierto
Palabra clave:Continuous piecewise linear differential system
Phase portrait
Limit cycle
Poincaré disc
Descripción
Sumario: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.