Global dynamics of the Selkov systems
The aim of this paper is to investigate the problem of limit cycles and global dynamics for the general case of the Selkov system. By applying limit cycle theory for Liénard systems, we first transform the Selkov systems into Liénard systems. Then the theory and techniques related to limit cycles fo...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:326009 |
| Acceso en línea: | https://ddd.uab.cat/record/326009 https://dx.doi.org/urn:doi:10.1016/j.physd.2025.134894 |
| Access Level: | acceso embargado |
| Palabra clave: | Limit cycle Degenerate Hopf bifurcation Generalized heteroclinic loop Selkov system Liénard system |
| Sumario: | The aim of this paper is to investigate the problem of limit cycles and global dynamics for the general case of the Selkov system. By applying limit cycle theory for Liénard systems, we first transform the Selkov systems into Liénard systems. Then the theory and techniques related to limit cycles for Liénard systems can be utilized and further developed. We obtain a new criterion for the uniqueness of limit cycles in general Liénard systems. Consequently, we address the majority of parameter cases for the conjecture regarding the uniqueness of limit cycles proposed in the literature. Finally, we present the global bifurcations and dynamical structures of the system in the Poincaré disc. |
|---|