On the global behavior of the rational difference equation \(y_{n+1}=\frac{\alpha_n+y_{n-r}}{\alpha_n+y_{n-k}}\)

Year 2022, Volume: 5 Issue: 3, 312 - 324, 30.09.2022

Sihem Oudina Mohamed Amine Kerker , Abdelouahab Salmi

https://doi.org/10.53006/rna.974156

https://izlik.org/JA98MD82XW

Abstract

In this article, we study the global behavior of the following higher-order nonautonomous rational difference equation
\[
y_{n+1}=\frac{\alpha_n+y_{n-r}}{\alpha_n+y_{n-k}},\quad n=0,1,...,
\]
where \(\left\{\alpha_n\right\}_{n\geq0}\) is a bounded sequence of
positive numbers, \(k,r\) are nonnegative integers such that \(r

Keywords

Rational difference equation , oscillation , local stability , global attractivity

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