Final Evolutions for Lotka-Volterra Systems in R3 Having a Darboux Invariant
The Lotka-Volterra systems have been studied intensively due to their applications. While the phase portraits of the 2-dimensional Lotka-Volterra systems have been classified, this is not the case for the ones in dimension three. Here we classify all the 3-dimensional Lotka-Volterra systems having a...
| Autores: | , |
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| 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:312565 |
| Acceso en línea: | https://ddd.uab.cat/record/312565 https://dx.doi.org/urn:doi:10.58997/ejde.2025.37 |
| Access Level: | acceso abierto |
| Palabra clave: | Lotka-Volterra systems Darboux invariants Global dynamics Poincare compactification |
| Sumario: | The Lotka-Volterra systems have been studied intensively due to their applications. While the phase portraits of the 2-dimensional Lotka-Volterra systems have been classified, this is not the case for the ones in dimension three. Here we classify all the 3-dimensional Lotka-Volterra systems having a Darboux invariant of the form x1y2z3e, where λ, s ∈ R and s(λ123) ≠ 0. The existence of such kind of Darboux invariants in a differential system allow to determine the α-limits and ω-limits of all the orbits of the differential system. For this class of Lotka-Volterra systems we can describe completely their phase portraits in the Poincaré ball. As an application we illustrate with an example one of these phase portraits. |
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