Crossing limit cycles for discontinuous piecewise linear differential centers separated by three parallel straight lines
In this paper we study the continuous and discontinuous planar piecewise differential systems formed by four linear centers separated by three parallel straight lines denoted by Σ = {(x,y) ∈ R2 : x = -p, x = 0, x = q, p, q > 0}. We prove that when these piecewise differential systems are continuo...
| Autores: | , , , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2023 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:307742 |
| Acesso em linha: | https://ddd.uab.cat/record/307742 https://dx.doi.org/urn:doi:10.1007/s12215-022-00766-3 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Limit cycles Linear centers Continuous piecewise differential systems Discontinuous piecewise differential systems First integrals |
| Resumo: | In this paper we study the continuous and discontinuous planar piecewise differential systems formed by four linear centers separated by three parallel straight lines denoted by Σ = {(x,y) ∈ R2 : x = -p, x = 0, x = q, p, q > 0}. We prove that when these piecewise differential systems are continuous they have no limit cycles. While for the discontinuous case we show that they can have at most four limit cycles and we also provide examples of such systems with zero, one, and two limit cycles. In particular we have solved the extension of the 16th Hilbert problem to this class of piecewise differential systems. |
|---|