Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems witha a straight line of separation
In this paper we study the maximum number of limit cycles for planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line. Here we only consider non-sliding limit cycles. For that systems, the interior of any limit cycle only contains a unique s...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2013 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:150641 |
| Acesso em linha: | https://ddd.uab.cat/record/150641 https://dx.doi.org/urn:doi:10.1142/S0218127413500661 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Non-smooth differential system Limit cycle Piecewise linear differential system |
| Resumo: | In this paper we study the maximum number of limit cycles for planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line. Here we only consider non-sliding limit cycles. For that systems, the interior of any limit cycle only contains a unique singular point or a unique sliding segment. Moreover, the linear differential systems that we consider in every half-plane can have either a focus (F), or a node (N), or a saddle (S), these equilibrium points can be real or virtual. Then, we can consider six kinds of planar discontinuous piecewise linear differential systems: FF, FN, FS, NN, NS, SS. We analyze for each of these types of discontinuous differential systems the maximum number of known limit cycles. |
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