Stability of singular limit cycles for Abel equations
We obtain a criterion for determining the stability of singular limit cycles of Abel equations x = A(t)x3 + B(t)x2 . This stability controls the possible saddle-node bifurcations of limit cycles. Therefore, studying the Hopf-like bifurcations at x = 0, together with the bifurcations at infinity of a...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:145334 |
| Acceso en línea: | https://ddd.uab.cat/record/145334 https://dx.doi.org/urn:doi:10.3934/dcds.2015.35.1873 |
| Access Level: | acceso abierto |
| Palabra clave: | Abel equation Closed solution Limit cycles Periodic solutions |
| Sumario: | We obtain a criterion for determining the stability of singular limit cycles of Abel equations x = A(t)x3 + B(t)x2 . This stability controls the possible saddle-node bifurcations of limit cycles. Therefore, studying the Hopf-like bifurcations at x = 0, together with the bifurcations at infinity of a suitable compactification of the equations, we obtain upper bounds of their number of limit cycles. As an illustration of this approach, we prove that the family x = at(t-tA )x3 +b(t-tB )x2 , with a, b. |
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