On construction of almost periodic sequences and applications to some discrete population models

Hamidoğlu A., Taghiyev M. H.

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, vol.27, no.1, pp.118-131, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1080/10236198.2021.1876039
  • Journal Name: JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.118-131
  • Keywords: almost periodic functions, diophantine approximation, Dirichlet's theorem, Kronecker's theorem, logistic equation, Lotka–Volterra equation, rationally independent numbers
  • Yıldız Technical University Affiliated: Yes

Abstract

In this work, we develop a novel approximation strategy for building almost periodic sequences in the theory of almost periodic functions. Here, we create a different perspective for the argument of Dirichlet in the theory of numbers and design an integer approximation strategy in this regard. The idea behind the strategy comes from Kronecker's theorem and it is proven that for given an almost periodic function, it is possible to design its corresponding almost periodic sequence. Moreover, we provide two population models in both continuous and discrete cases where almost periodic sequence solutions are designed under suitable circumstances.