Phase portraits of a family of Kolmogorov systems depending on six parameters
We consider a general 3-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xi yj zk. The restriction of this Lotka-Volterra system to each surface H(x, y, z) = h varying h ∈ R provide Kolmogorov systems. With the additional assumption that they have a Darb...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:258885 |
| Acesso em linha: | https://ddd.uab.cat/record/258885 |
| Access Level: | acceso abierto |
| Palavra-chave: | Kolmogorov system Lotka-Volterra system Phase portrait Poincaré disc |
| Resumo: | We consider a general 3-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xi yj zk. The restriction of this Lotka-Volterra system to each surface H(x, y, z) = h varying h ∈ R provide Kolmogorov systems. With the additional assumption that they have a Darboux invariant of the form xl ym est they reduce to the Kolmogorov systems x˙ = x (a0 - µ(c1x + c2z2 + c3z)), z˙ = z (c0 + c1x + c2z2 + c3z)). We classify the phase portraits in the Poincaré disc of all these Kolmogorov systems which depend on six parameters. |
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