Repositori institucional URV
| Author, as appears in the article.: | Marín, David; Queiroz, Lucas; Villadelprat, Jordi |
| Author's mail: | jordi.villadelprat@urv.cat |
| Journal publication year: | 2024 |
| Publication Type: | info:eu-repo/semantics/article |
| ISSN: | 0214-1493 |
| Abstract: | We consider smooth families of planar polynomial vector fields {Xμ}μ∈Λ, where Λ is an open subset of RN, for which there is a hyperbolic polycycle Γ that is persistent (i.e., such that none of the separatrix connections is broken along the family). It is well known that in this case the cyclicity of Γ at μ0 is zero unless its graphic number r(μ0) is equal to one. It is also well known that if r(μ0)=1 (and some generic conditions on the return map are verified) then the cyclicity of Γ at μ0 is one, i.e., exactly one limit cycle bifurcates from Γ. In this paper we prove that this limit cycle approaches Γ exponentially fast and that its period goes to infinity as 1/|r(μ)−1| when μ→μ0. Moreover, we prove that if those generic conditions are not satisfied, although the cyclicity may be exactly 1, the behavior of the period of the limit cycle is not determined. |
| Article's DOI: | 10.48550/arXiv.2306.15473 |
| Link to the original source: | https://arxiv.org/abs/2306.15473 |
| Papper version: | info:eu-repo/semantics/acceptedVersion |
| licence for use: | https://creativecommons.org/licenses/by/3.0/es/ |
| Department: | Enginyeria Informàtica i Matemàtiques |
| Funding program: | Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos |
| Funding program action: | Proyectos I+D Generación de Conocimiento |
| Acronym: | ATBiD |
| Project code: | PID2020-118281GB-C33 |
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