Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles tha...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:199322 |
| Acesso em linha: | https://ddd.uab.cat/record/199322 https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.07.024 |
| Access Level: | acceso abierto |
| Palavra-chave: | Discontinuous piecewise linear differential system Limit cycle Non-smooth differential system |
| Resumo: | From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles. |
|---|