Limit cycles bifurcanting from the period annulus of a uniform isochronous center in a quartic polynomial differential system
We study the number of limit cycles that bifurcate from the periodic solutions surrounding a uniform isochronous center located at the origin of the quartic polynomial differential system =-y xy(x^2 y^2), =x y^2(x^2 y^2), when it is perturbed inside the class of all quartic polynomial differential s...
| Autores: | , |
|---|---|
| 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:145311 |
| Acceso en línea: | https://ddd.uab.cat/record/145311 |
| Access Level: | acceso abierto |
| Palabra clave: | Averaging theory Limit cycles Periodic orbit Polynomial vector field Uniform isochronous center |
| Sumario: | We study the number of limit cycles that bifurcate from the periodic solutions surrounding a uniform isochronous center located at the origin of the quartic polynomial differential system =-y xy(x^2 y^2), =x y^2(x^2 y^2), when it is perturbed inside the class of all quartic polynomial differential systems. Using the averaging theory of first order we show that at least 8 limit cycles can bifurcate from the period annulus of the considered center. Recently this problem was studied in Electron. J. Differ. Equ. 95 (2014), 1--14 where the authors only found 3 limit cycles. |
|---|