Limit cycles for discontinuous quadratic differential systems with two zones
In this paper we study the maximum number of limit cycles given by the averaging theory of first order for discontinuous differential systems, which can bifurcate from the periodic orbits of the quadratic isochronous centers ˙x = -y + x2, ˙y = x + xy and ˙x = -y + x2 - y2, y˙ = x + 2xy when they are...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150734 |
| Acesso em linha: | https://ddd.uab.cat/record/150734 https://dx.doi.org/urn:doi:10.1016/j.jmaa.2013.12.031 |
| Access Level: | acceso abierto |
| Palavra-chave: | Limit cycles Discontinuous quadratic systems Averaging theory Isochronous center |
| Resumo: | In this paper we study the maximum number of limit cycles given by the averaging theory of first order for discontinuous differential systems, which can bifurcate from the periodic orbits of the quadratic isochronous centers ˙x = -y + x2, ˙y = x + xy and ˙x = -y + x2 - y2, y˙ = x + 2xy when they are perturbed inside the class of all discontinuous quadratic polynomial differential systems with the straight line of discontinuity y = 0. Comparing the obtained results for the discontinuous with the results for the continuous quadratic polynomial differential systems, this work shows that the discontinuous systems have at least 3 more limit cycles surrounding the origin than the continuous ones. |
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