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

Authors : Merve Kara, Nouressedat Touafek, Yasin Yazlik

Pages : 767-778

Doi:10.35378/gujs.641441

View : 18 | Download : 11

Publication Date : 2020-09-01

Article Type : Research

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