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Phase Portraits of the Leslie-Gower System

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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 ℝ2 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.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain

    Jaume Llibre

  2. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    Claudia Valls

Authors
  1. Jaume Llibre
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  2. Claudia Valls
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Corresponding author

Correspondence to Claudia Valls.

Additional information

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.

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Llibre, J., Valls, C. Phase Portraits of the Leslie-Gower System. Acta Math Sci 42, 1734–1742 (2022). https://doi.org/10.1007/s10473-022-0502-4

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  • DOI: https://doi.org/10.1007/s10473-022-0502-4

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