A Generalised Difference Equation and Its Dynamics and Solutions

KARATAŞ R., Gelişken A., Arı M.

Mathematics, vol.12, no.22, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 22
  • Publication Date: 2024
  • Doi Number: 10.3390/math12223531
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: boundedness, difference equation, globally asymptotically, periodicity, stability
  • Akdeniz University Affiliated: Yes

Abstract

Rational difference equations have a wide range of applications in various fields of science. To illustrate, the equation (Formula presented.), known as the Riccati difference equation, has been applied in the field of optics. In this study, the global asymptotic stability of the difference equation (Formula presented.), is proved. The solutions of this difference equation are obtained by applying the standard iteration method, and the periodicity of these solutions is determined. Furthermore, this difference equation represents a generalisation of the results obtained in previous studies.