On a Higher-Order Rational Difference Equation

Abstract

In this paper, we investigate the global behavior of the solutions of the difference equationwith non-negative initial conditions, the parameters A, B are non-negative real numbers, C, D are positive real numbers, k, l are fixed non-negative integers such that l ≤ k, and m i , i = l, k are positive integers.

Stability analysis for a rational difference equation

“…Among these are refs. (Abdelrahman, 2019;Abdelrahman, Chatzarakis, Tongxing, & Osama, 2018;Almatrafi, Elsayed, & Alzahrani, 2019;Almatrafi, Elsayed, & Alzahrani, 2018;Belhannache, Touafek, & Abo-Zeid, 2016;Elabbasy, El-Metawally, & Elsayed, 2008;El-Moneam & Zayed, 2014;Khaliq & Hassan, 2018;Khyat, & Kulenovi c, 2017;Kocic & Ladas, 1993;Kostrov & Kudlak, 2016;Liu, Li, Han, & Zhong, 2018;Moranjki c & Nurkanovi c, 2017;Saleh & Aloqeili, 2005;Simsek, Cinar, & Yalcinkaya, 2006). It is the fundamental aim of this work to discuss some mathematical aspects, for example the stability and boundedness, for the following recursive equation:…”

On a solvable system of difference equations of higher-order with period two coefficients

“…Theory of di¤erence equations have attracted attention of many authors in recent years(see, e.g., [1]- [40]). Most of the recent applications of this theory have appeared in many scienti…c areas such as biology, physics, engineering, economics.…”

Qualitative study of a higher order rational difference equation

“…Many researchers have investigated the behavior of the solution of difference equations for example: Cinar [6] has obtained the solutions of the following difference equation…”

“…where α is the immigration rate and β is the population growth rate. The generalized Beverton-Holt stock recruitment model has investigated in [5]:…”

“…See also [1]- [5], [30]- [45]. Other related results on rational dierence equations can be found in refs.…”