Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity

Érika Diz-Pita; Jaume Llibre; M. Victoria Otero-Espinar

doi:10.1016/j.cnsns.2021.106038

Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity

Érika Diz-Pita^*, Jaume Llibre, M. Victoria Otero-Espinar

^*Autor corresponent d’aquest treball

Departament de Matemàtiques

Universidade de Santiago de Compostela (USC)

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Resum

We give the topological classification of the global phase portraits in the Poincaré disc of the Kolmogorov systems ẋ=xa₀+c₁x+c₂z²+c₃z,ż=zc₀+c₁x+c₂z²+c₃z,which depend on five parameters and have infinitely many singular points at the infinity. We prove that these systems have 22 topologically distinct phase portraits.

Idioma original	Anglès
Número d’article	106038
Revista	Communications in Nonlinear Science and Numerical Simulation
Volum	104
DOIs	https://doi.org/10.1016/j.cnsns.2021.106038
Estat de la publicació	Publicada - de gen. 2022

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10.1016/j.cnsns.2021.106038

https://ddd.uab.cat/record/257095

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title = "Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity",

abstract = "We give the topological classification of the global phase portraits in the Poincar{\'e} disc of the Kolmogorov systems ẋ=xa0+c1x+c2z2+c3z,{\.z}=zc0+c1x+c2z2+c3z,which depend on five parameters and have infinitely many singular points at the infinity. We prove that these systems have 22 topologically distinct phase portraits.",

keywords = "Kolmogorov system, Phase portrait, Poincar{\'e} disc",

author = "{\'E}rika Diz-Pita and Jaume Llibre and Otero-Espinar, \{M. Victoria\}",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2022",

month = jan,

doi = "10.1016/j.cnsns.2021.106038",

language = "English",

volume = "104",

journal = "Communications in Nonlinear Science and Numerical Simulation",

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publisher = "Elsevier",

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TY - JOUR

T1 - Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity

AU - Diz-Pita, Érika

AU - Llibre, Jaume

AU - Otero-Espinar, M. Victoria

PY - 2022/1

Y1 - 2022/1

N2 - We give the topological classification of the global phase portraits in the Poincaré disc of the Kolmogorov systems ẋ=xa0+c1x+c2z2+c3z,ż=zc0+c1x+c2z2+c3z,which depend on five parameters and have infinitely many singular points at the infinity. We prove that these systems have 22 topologically distinct phase portraits.

AB - We give the topological classification of the global phase portraits in the Poincaré disc of the Kolmogorov systems ẋ=xa0+c1x+c2z2+c3z,ż=zc0+c1x+c2z2+c3z,which depend on five parameters and have infinitely many singular points at the infinity. We prove that these systems have 22 topologically distinct phase portraits.

KW - Kolmogorov system

KW - Phase portrait

KW - Poincaré disc

UR - https://www.scopus.com/pages/publications/85115031865

U2 - 10.1016/j.cnsns.2021.106038

DO - 10.1016/j.cnsns.2021.106038

M3 - Article

AN - SCOPUS:85115031865

SN - 1007-5704

VL - 104

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 106038

ER -

Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity

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