Planar Kolmogorov systems with infinitely many singular points at infinity

We classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at infinity. We give the...

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Detalhes bibliográficos
Autores: Diz-Pita, Érika|||0000-0002-7086-6614, Llibre, Jaume|||0000-0002-9511-5999, Otero-Espinar, M. Victoria|||0000-0002-0201-0523
Formato: artículo
Fecha de publicación:2022
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:274780
Acesso em linha:https://ddd.uab.cat/record/274780
https://dx.doi.org/urn:doi:10.1142/S0218127422500651
Access Level:acceso abierto
Palavra-chave:Kolmogorov system
Lotka-Volterra system
Phase portrait
Poincaré disc
Descrição
Resumo:We classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at infinity. We give the topological classification of their phase portraits in the Poincaré disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.