4.7 Article

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

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ELSEVIER
DOI: 10.1016/j.cnsns.2021.106038

Keywords

Kolmogorov system; Phase portrait; Poincare disc

Funding

  1. Ministerio de Ciencia e Innovacion, Agencia Estatal de Inves-tigacion (Spain) [PID2020-115155GB-I00]
  2. Conselleria de Educacion, Universidade e Formacion Profesional (Xunta de Galicia) [ED431C 2019/10]
  3. FEDER funds
  4. Ministerio de Educacion, Cultura y Deporte de Espana [FPU17/02125]
  5. Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigacion [PID2019-104658GB-I00]
  6. Agencia de Gestio d'Ajuts Universitaris i de Recerca grant [2017SGR1617]
  7. H2020 European Research Council [MSCA-RISE-2017-777911]

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The study provided a topological classification of the global phase portraits of Kolmogorov systems in the Poincare disc, revealing a total of 22 topologically distinct phase portraits.
We give the topological classification of the global phase portraits in the Poincare disc of the Kolmogorov systems x = x z = z (a0 + c1x + c2z2 + c3z) , (c0 + 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. (c) 2021 Elsevier B.V. All rights reserved.

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