Planar Kolmogorov systems with infinitely many singular points at infinity
Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)

Date:	2022
Abstract:	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.
Grants:	Agencia Estatal de Investigación PID2020-115155GB-I00 Ministerio de Educación, Cultura y Deporte FPU17/02125 Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Note:	Altres ajuts: Consellería de Educación, Universidade e Formación Profesional (Xunta de Galicia), grant ED431C 2019/10
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Kolmogorov system ; Lotka-Volterra system ; Phase portrait ; Poincaré disc
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 5 (April 2022) , art. 2250065, ISSN 1793-6551

DOI: 10.1142/S0218127422500651

Postprint 14 p, 1.1 MB

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