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Attraction in Nonmonotone Planar Systems and Real-Life Models

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Abstract

Let \(h:V\subset {\mathbb {R}}^{2}\longrightarrow {\mathbb {R}}^{2}\) be an embedding. The aim of this paper is to analyze the dynamical behavior of h depending on the number of fixed points and 2-cycles, their local behaviors and the features of V. Our approach allows us to extend some celebrated results of the theory of monotone flows, namely the order interval trichotomy, for non-monotone maps. Moreover, we discuss several applications in classical models. In the particular case of the Ricker system, we recover some recent results deduced from computer assistance.

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Acknowledgements

I would like to thank prof. R. Ortega and the referee for many suggestions and indications on this paper.

Funding

The funding was provided by Ministerio de Educación, Cultura y Deporte (Grant No. MTM2017-839737238).

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Oviedo, Oviedo, Spain

    Alfonso Ruiz-Herrera

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  1. Alfonso Ruiz-Herrera
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Correspondence to Alfonso Ruiz-Herrera.

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Dedicated to Prof. Rafael Ortega on the occasion of his 60th birthday

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Ruiz-Herrera, A. Attraction in Nonmonotone Planar Systems and Real-Life Models. J Dyn Diff Equat 34, 919–943 (2022). https://doi.org/10.1007/s10884-020-09893-w

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  • DOI: https://doi.org/10.1007/s10884-020-09893-w

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