On the periodicity of the solution of a rational difference equation
No Thumbnail Available
Files
Date
2019-08-01
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi Fen Fakültesi
Abstract
In this paper, some cases on the periodicity of the rational difference equation
S_{n+1}=S_{n-p}(((aS_{n-q}+bS_{n-r}+cS_{n-s})/(dS_{n-q}+eS_{ n-r}+fS_{n-s}))),
are investigated, where a, b, c, d, e, f ∈(0,∞). The initial conditions S_{-p}, S_{-p+1},...,S_{-q}, S_{-q+1},...,S_{-r}, S_{-r+1},...,S_{-s},...,S_{-s+1},...,S₋₁ and S₀ are arbitrary positive real numbers such that p>q>r>s≥0. Some numerical examples are provided to illustrate the theoretical discussion.
Description
Keywords
Rational difference equations, Periodicity, Higher-order