On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
While the limit cycles of the discontinuous piecewise differential systems formed by two linear differential systems separated by one straight line have been studied intensively, and up to now there are examples of these systems with at most 3 limit cycles. There are almost no works studying the lim...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:267136 |
| Acceso en línea: | https://ddd.uab.cat/record/267136 https://dx.doi.org/urn:doi:10.1016/j.chaos.2022.112256 |
| Access Level: | acceso abierto |
| Palabra clave: | Linear focus Linear center Quadratic weak focus Quadratic center Limit cycle Discontinuous piecewise differential system |
| Sumario: | While the limit cycles of the discontinuous piecewise differential systems formed by two linear differential systems separated by one straight line have been studied intensively, and up to now there are examples of these systems with at most 3 limit cycles. There are almost no works studying the limit cycles of the discontinuous piecewise differential systems formed by one linear differential system and a quadratic polynomial differential system separated by one straight line. In this paper using the averaging theory up to seven order we prove that the discontinuous piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center separated by one straight line can have 8 limit cycles. More precisely, at every order of the averaging theory from order one to order seven we provide the maximum number of limit cycles that can be obtained using the averaging theory. |
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