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

  1. Érika Diz-Pita 1
  2. Jaume Llibre 2
  3. M. Victoria Otero-Espinar 1
  1. 1 Universidade de Santiago de Compostela, Santiago de Compostela, Spain
  2. 2 Universitat Autònoma de Barcelona, Barcelona, Spain
Libro:
Computational and Mathematical Models in Biology

Editorial: Springer Link

ISSN: 2195-9994,  2196-0003

ISBN: 9783031426889,  9783031426896

Ano de publicación: 2023

Páxinas: 103-128

Tipo: Capítulo de libro

DOI: 10.1007/978-3-031-42689-6 GOOGLE SCHOLAR lock_openAcceso aberto editor

Resumo

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.