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

^*Corresponding author for this work

Department of Mathematics

Universidade de Santiago de Compostela (USC)

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Article number	106038
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	104
DOIs	https://doi.org/10.1016/j.cnsns.2021.106038
Publication status	Published - Jan 2022

Keywords

Kolmogorov system
Phase portrait
Poincaré disc

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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\}",

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language = "English",

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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

Abstract

Keywords

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