PHASE PORTRAITS OF THE LESLIE-GOWER SYSTEM

PHASE PORTRAITS OF THE LESLIE-GOWER SYSTEM

PHASE PORTRAITS OF THE LESLIE-GOWER SYSTEM

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doi:10.1007/s10473-022-0502-4

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (5): 1734-1742.doi: 10.1007/s10473-022-0502-4

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Jaume LLIBRE¹, Claudia VALLS²

1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain;
2. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

Received:2021-05-12 Revised:2021-12-08 Published:2022-11-02
Contact: Claudia Valls,E-mail:cvalls@math.tecnico.ulisboa.pt E-mail:cvalls@math.tecnico.ulisboa.pt
Supported by:
The first author was supported by the Agencia Estatal de Investigación grant PID2019-104658GB-I00 and the H2020 European Research Council grant MSCA-RISE-2017-777911. The second author was partially supported by FCT/Portugal through CAMGSD, IST-ID, projects UIDB/04459/2020 and UIDP/04459/2020.

Abstract: In this paper we characterize the phase portraits of the Leslie-Gower model for competition among species. We give the complete description of their phase portraits in the Poincaré disc (i.e., in the compactification of $\mathbb{R}^2$ adding the circle $\mathbb{S}^1$ of the infinity) modulo topological equivalence.
It is well-known that the equilibrium point of the Leslie-Gower model in the interior of the positive quadrant is a global attractor in this open quadrant, and in this paper we characterize where the orbits attracted by this equilibrium born.

Key words: predator-prey models, Leslie-Gower system, Poincaré compactification, global phase portraits

CLC Number:

34A05

Jaume LLIBRE, Claudia VALLS. PHASE PORTRAITS OF THE LESLIE-GOWER SYSTEM[J].Acta mathematica scientia,Series B, 2022, 42(5): 1734-1742.

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