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Study of the Nonelementary Singular Points and the Dynamics Near the Infinity in Predator-Prey Systems

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Computational and Mathematical Models in Biology

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 38))

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Abstract

In this chapter, we present the results obtained in two predator-prey systems, paying special attention to the dynamics near the infinity and the nonelementary singular points. First, the desingularization technique known as blow-up technique allows one to study any type of singularities of analytic systems in dimension two even if they are not elementary. In the other hand, the introduction of the Poincaré compactification allows one to accomplish a complete study of the global dynamics of these systems. In addition to the proofs of the results obtained in those cases, we include a survey on the used techniques from a theoretical point of view.

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Authors and Affiliations

  1. Universidade de Santiago de Compostela, Santiago de Compostela, Spain

    Érika Diz-Pita & M. Victoria Otero-Espinar

  2. Universitat Autònoma de Barcelona, Barcelona, Spain

    Jaume Llibre

Authors
  1. Érika Diz-Pita
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  2. Jaume Llibre
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  3. M. Victoria Otero-Espinar
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Corresponding author

Correspondence to Érika Diz-Pita .

Editor information

Editors and Affiliations

  1. School of Engineering, Center of Mathematics, Polytechnic of Porto, Porto, Portugal

    Carla M.A. Pinto

  2. Faculty of Engineering and Architecture, Ghent University, Ghent, Belgium

    Clara Mihaela Ionescu

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Diz-Pita, É., Llibre, J., Otero-Espinar, M.V. (2023). Study of the Nonelementary Singular Points and the Dynamics Near the Infinity in Predator-Prey Systems. In: Pinto, C.M., Ionescu, C.M. (eds) Computational and Mathematical Models in Biology. Nonlinear Systems and Complexity, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-031-42689-6_5

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