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...
| Autores: | , |
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| 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 |
| 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. |
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