Planar Kolmogorov Systems with Infinitely Many Singular Points at Infinity

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

doi:10.1142/S0218127422500651

Planar Kolmogorov Systems with Infinitely Many Singular Points at Infinity

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

Department of Mathematics

Universidade de Santiago de Compostela (USC)

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

Abstract

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

Original language	English
Article number	2250065
Number of pages	14
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	32
Issue number	5
DOIs	https://doi.org/10.1142/S0218127422500651
Publication status	Published - 1 Apr 2022

Keywords

Kolmogorov system
Lotka-Volterra system
Poincaré disc
phase portrait

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10.1142/S0218127422500651

https://ddd.uab.cat/record/274780

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title = "Planar Kolmogorov Systems with Infinitely Many Singular Points at Infinity",

abstract = "We classify the global dynamics of the five-parameter family of planar Kolmogorov systems C = 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 inifnity. We give the topological classification of their phase portraits in the Poincar{\'e} disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.",

keywords = "Kolmogorov system, Lotka-Volterra system, Poincar{\'e} disc, phase portrait",

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T1 - Planar Kolmogorov Systems with Infinitely Many Singular Points at Infinity

AU - Diz-Pita, Érika

AU - Llibre, Jaume

AU - Otero-Espinar, M. Victoria

PY - 2022/4/1

Y1 - 2022/4/1

N2 - We classify the global dynamics of the five-parameter family of planar Kolmogorov systems C = y(b0 + b1yz + b2y + b3z),ż = z(c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at inifnity. 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.

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

KW - Kolmogorov system

KW - Lotka-Volterra system

KW - Poincaré disc

KW - phase portrait

UR - https://www.scopus.com/pages/publications/85129295161

U2 - 10.1142/S0218127422500651

DO - 10.1142/S0218127422500651

M3 - Article

AN - SCOPUS:85129295161

SN - 0218-1274

VL - 32

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 5

M1 - 2250065

ER -

Planar Kolmogorov Systems with Infinitely Many Singular Points at Infinity

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