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

2020 ◽  
pp. 1-1
Author(s):  
Merve KARA ◽  
Nouressedat TOUAFEK ◽  
Yasin YAZLİK
Keyword(s):  
Difference Equations ◽  
Three Dimensional ◽  
Dimensional System ◽  
System Of Difference Equations ◽  
Three Dimensional System

scholarly journals On a solvable three-dimensional system of difference equations

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1167-1186
Author(s):  
Merve Kara ◽  
Yasin Yazlik
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Three Dimensional ◽  
Asymptotic Behavior Of Solutions ◽  
Dimensional System ◽  
Real Numbers ◽  
System Of Difference Equations ◽  
Initial Values ◽  
Forbidden Set ◽  
Three Dimensional System

In this paper, we show that the following three-dimensional system of difference equations xn = zn-2xn-3/axn-3 + byn-1, yn = xn-2yn-3/cyn-3 + dzn-1, zn = yn-2zn-3/ezn-3+ fxn-1, n ? N0, where the parameters a, b, c, d, e, f and the initial values x-i, y-i, z-i, i ? {1, 2, 3}, are real numbers, can be solved, extending further some results in literature. Also, we determine the asymptotic behavior of solutions and the forbidden set of the initial values by using the obtained formulas.

Solvability of a nonlinear three-dimensional system of difference equations with constant coefficients

2021 ◽  
Vol 71 (5) ◽  
pp. 1133-1148
Author(s):  
Merve Kara ◽  
Yasin Yazlik
Keyword(s):  
Difference Equations ◽  
Three Dimensional ◽  
Complex Numbers ◽  
Dimensional System ◽  
System Of Difference Equations ◽  
Initial Values ◽  
Constant Coefficients ◽  
Forbidden Set ◽  
Three Dimensional System

Abstract In this paper, we show that the following three-dimensional system of difference equations x n + 1 = y n x n − 2 a x n − 2 + b z n − 1 , y n + 1 = z n y n − 2 c y n − 2 + d x n − 1 , z n + 1 = x n z n − 2 e z n − 2 + f y n − 1 , n ∈ N 0 , $$\begin{equation*} x_{n+1}=\frac{y_{n}x_{n-2}}{ax_{n-2}+bz_{n-1}}, \quad y_{n+1}=\frac{z_{n}y_{n-2}}{cy_{n-2}+dx_{n-1}}, \quad z_{n+1}=\frac{x_{n}z_{n-2}}{ez_{n-2}+fy_{n-1}}, \quad n\in \mathbb{N}_{0}, \end{equation*}$$ where the parameters a, b, c, d, e, f and the initial values x −i , y −i , z −i , i ∈ {0, 1, 2}, are complex numbers, can be solved, extending further some results in the literature. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, an application concerning a three-dimensional system of difference equations are given.

scholarly journals On the Behavior of a System of Rational Difference Equationsxn+1=xn-1/(ynxn-1-1),yn+1=yn-1/(xnyn-1-1),zn+1=1/xnzn-1

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Liu Keying ◽  
Wei Zhiqiang ◽  
Li Peng ◽  
Zhong Weizhou
Keyword(s):  
Difference Equations ◽  
Three Dimensional ◽  
Dimensional System ◽  
Rational Difference Equations ◽  
Initial Values ◽  
Three Dimensional System

We are concerned with a three-dimensional system of rational difference equations with nonzero initial values. We present solutions of the system in an explicit way and obtain the asymptotical behavior of solutions.

scholarly journals More on Three-Dimensional Systems of Rational Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Liu Keying ◽  
Zhao Zhongjian ◽  
Li Xiaorui ◽  
Li Peng
Keyword(s):  
Difference Equations ◽  
Three Dimensional ◽  
Dimensional System ◽  
Rational Difference Equations ◽  
Three Dimensional System

We are concerned with a kind of three-dimensional system of rational difference equations, given by Kurbanli (2011). A new expression of solution of the system is presented, and the asymptotical behavior is described. At the same time, we also consider a different system and obtain some results, which expand the study of such a kind of difference equations and the method can be applied to other systems.

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