On the limit cycles of a quartic model for Evolutionary Stable Strategies
This paper studies the number of centers and limit cycles of the family of planar quartic polynomial vector fields that has the invariant algebraic curve (4x2−1)(4y2−1)=0. The main interest for this type of vector fields comes from their appearance in some mathematical models in Game Theory composed...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/303228 |
| Acceso en línea: | http://dx.doi.org/10.1016/j.nonrwa.2024.104313 https://hdl.handle.net/11449/303228 |
| Access Level: | acceso abierto |
| Palabra clave: | Berlinskiĭ’s theorem Center-focus Cyclicity Evolutionary Stable Strategies Limit cycles Evolutionary stable strategies Invariant algebraic curves Limit-cycle Number of centers Polynomial vector field Quartic polynomial Vector fields |
| Sumario: | This paper studies the number of centers and limit cycles of the family of planar quartic polynomial vector fields that has the invariant algebraic curve (4x2−1)(4y2−1)=0. The main interest for this type of vector fields comes from their appearance in some mathematical models in Game Theory composed by two players. In particular, we find examples with five nested limit cycles surrounding the same singularity, as well as examples with four limit cycles formed by two disjoint nests, each one of them with two limit cycles. We also prove a Berlinskiĭ’s type result for this family of vector fields. |
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