Three nested limit cycles in discontinuous piecewise linear differential systems with two zones
In this paper we study a planar piecewise linear differential system formed by two regions separated by a straight line so that one system has a real unstable focus and the other a virtual stable focus which coincides with the real one. This system was introduced by S.-M. Huan and X.-S. Yang in [8]...
| Autores: | , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2012 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:150531 |
| Acesso em linha: | https://ddd.uab.cat/record/150531 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Non-smooth differential system Limit cycle Piecewise linear differential system |
| Resumo: | In this paper we study a planar piecewise linear differential system formed by two regions separated by a straight line so that one system has a real unstable focus and the other a virtual stable focus which coincides with the real one. This system was introduced by S.-M. Huan and X.-S. Yang in [8] who numerically showed that it can exhibit 3 limit cycles surrounding the real focus. This is the first example that a non-smooth piecewise linear differential system with two zones can have 3 limit cycles surrounding a unique equilibrium. We provide a rigorous proof of this numerical result. |
|---|