Attractors in k-Dimensional Discrete Systems of Mixed Monotonicity

Ziyad AlSharawi ^[3] ; Jose S. Cánovas ^[1] ; Sadok Kallel ^[2]
1. [1] Universidad Politécnica de Cartagena
  
  Universidad Politécnica de Cartagena
  
  Cartagena, España
2. [2] American University of Sharjah
  
  American University of Sharjah
  
  Emiratos Árabes Unidos
3. [3] American University of Sharjah & Universidad Politécnica de Cartagena
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
Idioma: inglés
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Resumen
- 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.