Planar Kolmogorov Systems Coming from Spatial Lotka-Volterra Systems
In this paper, we classify the phase portraits in the Poincaré disc of all the Kolmogorov systems a = y(b0 + b1yz + b2y + b3z), ż = z(c0 - μ(b1yz + b2y + b3z)), which depend on six parameters. We prove that these systems have 52 topologically distinct phase portraits in the Poincaré disc. These syst...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:307728 |
| Acceso en línea: | https://ddd.uab.cat/record/307728 https://dx.doi.org/urn:doi:10.1142/S0218127421502011 |
| Access Level: | acceso abierto |
| Palabra clave: | Kolmogorov system Lotka-Volterra system Phase portrait Poincaré disc |
| Sumario: | In this paper, we classify the phase portraits in the Poincaré disc of all the Kolmogorov systems a = y(b0 + b1yz + b2y + b3z), ż = z(c0 - μ(b1yz + b2y + b3z)), which depend on six parameters. We prove that these systems have 52 topologically distinct phase portraits in the Poincaré disc. These systems are provided by a general three-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xiyjzk, restricted to each surface H(x,y,z) = h varying h a with the additional assumption that they have a Darboux invariant of the form yℓzmest. |
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