Limit cycles of continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center
Due to their applications to many physical phenomena during these last decades the interest for studying the continuous or discontinuous piecewise differential systems has increased strongly. The limit cycles play a main role in the study of any planar differential system. Up to now the major part o...
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| Tipo de documento: | Artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:ddd.uab.cat:299735 |
| Acceso en línea: | https://ddd.uab.cat/record/299735 https://dx.doi.org/urn:doi:10.3934/dcdss.2022034 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Continuous piecewise differential system Limit cycle Linear center Quadratic center |
| Sumario: | Due to their applications to many physical phenomena during these last decades the interest for studying the continuous or discontinuous piecewise differential systems has increased strongly. The limit cycles play a main role in the study of any planar differential system. Up to now the major part of papers which study the limit cycles of the planar piecewise differential systems have considered systems formed by two pieces separated by one straight line. Here we consider planar continuous piecewise differential systems separated by a parabola. We prove that the planar continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center have at most one limit cycle. Moreover there are systems in this class exhibiting one limit cycle. So in particular we have solved the extension of the 16th Hilbert problem to this class of differential systems. |
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