Attractors in k-Dimensional Discrete Systems of Mixed Monotonicity

  1. Ziyad AlSharawi 1
  2. Jose S. Cánovas 2
  3. Sadok Kallel 3
  1. 1 American University of Sharjah & Universidad Politécnica de Cartagena
  2. 2 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

  3. 3 American University of Sharjah
    info

    American University of Sharjah

    Sarja, Emiratos Árabes Unidos

    ROR https://ror.org/001g2fj96

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Zeitschrift:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Datum der Publikation: 2024

Ausgabe: 23

Nummer: 1

Art: Artikel

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Andere Publikationen in: Qualitative theory of dynamical systems

Zusammenfassung

We consider k-dimensional discrete-time systems of the form in which the map F is continuous and monotonic in each one of its arguments. We define a partial order on , compatible with the monotonicity of F, and then use it to embed the k-dimensional system into a 2k-dimensional system that is monotonic with respect to this poset structure. An analogous construction is given for periodic systems. Using the characteristics of the higher-dimensional monotonic system, global stability results are obtained for the original system. Our results apply to a large class of difference equations that are pertinent in a variety of contexts. As an application of the developed theory, we provide two examples that cover a wide class of difference equations, and in a subsequent paper, we provide additional applications of general interest.

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