Well-Defined Solutions of a Three-Dimensional System of Difference Equations

Year 2020, Volume: 33 Issue: 3, 767 - 778, 01.09.2020

Merve Kara , Nouressedat Touafek Yasin Yazlik

https://doi.org/10.35378/gujs.641441

Cited By: 9

Abstract

We show that the
three-dimensional system of difference equations

x_{n+1}=\frac{ax_{n}z_{n-1}}{z_{n}-\beta}+\gamma,  y_{n+1}=\frac{by_{n}x_{n-1}}{x_{n}-\gamma}+\alpha, z_{n+1}=\frac{cz_{n}y_{n-1}}{y_{n}-\alpha}+\beta,

where the parameters a,b,x, \alpha, \beta, \gamma  and the initial
conditions x_{-i}, y_{-i}, i\in\{0,1\}  are non-zero real
numbers, can be solved. Using the obtained formulas, we determine the asymptotic
behavior of solutions and give conditions for which periodic solutions exists.
Some numerical examples are given to demonstrate the theoretical results.

Keywords

Periodic solution, difference equation, three dimensional system of difference equations

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