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On a class of nonlinear rational systems of difference equations

AIMS Mathematics, 2023
In this paper, we construct and formulate the solutions and periodicity character of the following nonlinear rational systems of difference equations: $ \begin{equation} S_{n+1} = \dfrac{T_{n} S_{n-2}}{S_{n-2} + T_{n-1}},\quad T_{n+1} = \dfrac{S_{n ...
Ibraheem M. Alsulami, E. M. Elsayed
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On a System of Difference Equations [PDF]

Discrete Dynamics in Nature and Society, 2013
We have investigated the periodical solutions of the system of rational difference equations , and where .
Ozan Özkan, Abdullah Selçuk Kurbanli
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Periodicities of a System of Difference Equations [PDF]

Journal of Function Spaces, 2017
We study the periodicities of a system of difference equations xn+1=max1/xn,An/yn-k,yn+1=max1/yn,Bn/xn-k, where initial values (x-k,y-k),…,(x0,y0)∈(0,+∞)×(0,+∞).
Weizhen Quan, Miaoqiao Pan, Xiaopei Li
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On a Periodic System of Difference Equations [PDF]

Abstract and Applied Analysis, 2012
Here we give a very short and elegant proof of an extension of two recent results on global periodicity of two systems of difference equations in a work of Elsayed et al. 2012.
Stevo Stević, Josef Diblík, Bratislav Iričanin, Zdeněk Šmarda   +3 more
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New class of practically solvable systems of difference equations of hyperbolic-cotangent-type

Electronic Journal of Qualitative Theory of Differential Equations, 2020
The systems of difference equations $$x_{n+1}=\frac{u_nv_{n-2}+a}{u_n+v_{n-2}},\quad y_{n+1}=\frac{w_ns_{n-2}+a}{w_n+s_{n-2}},\quad n\in\mathbb{N}_0,$$ where $a, u_0, w_0, v_j, s_j$ $j=-2,-1,0,$ are complex numbers, and the sequences $u_n$, $v_n,$ $w_n$,
Stevo Stevic
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Behavior of an Exponential System of Difference Equations [PDF]

Discrete Dynamics in Nature and Society, 2014
We study the qualitative behavior of the following exponential system of rational difference equations: xn+1 = αe-yn+βe-yn-1/γ+αxn+βxn-1,  yn+1 = α1e-xn+β1e-xn-1/γ1+α1yn+β1yn-1,  n = 0,1,…, where α, β, γ, α1, β1, and γ1 and initial conditions x0,   x-1,  
A. Q. Khan, M. N. Qureshi
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On a system of difference equations of third order solved in closed form

Journal of Innovative Applied Mathematics and Computational Sciences, 2021
In this work, we show that the system of difference equations xn+1=(ayn-2xn-1yn+bxn-1yn-2+cyn-2+d)/(yn-2xn-1yn), yn+1=(axn-2yn-1xn+byn-1xn-2+cxn-2+d)/(xn-2yn-1xn), where n belongs to the set of positive integer numbers, x-2, x-1, x0, y-2, y-1 and y0 are ...
Youssouf AKROUR, Nouressadat Touafek, Yacine Halim   +2 more
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Periodic Solutions for a System of Difference Equations [PDF]

Discrete Dynamics in Nature and Society, 2009
This paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. The theorems are proved by using critical point theory.
Shugui Kang, Bao Shi
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Closed-form solutions of systems of nonlinear difference equations and their connections to generalized Fibonacci numbers and related sequences

AIMS Mathematics
In this work, we conducted a comprehensive analytical investigation of an extended nonlinear difference system, which can be regarded as a generalization of a classical nonlinear difference equation. The proposed extension introduces additional variables,
Hassan J. Al Salman
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On Some Solvable Systems of Some Rational Difference Equations of Third Order

Mathematics, 2023
Our aim in this paper is to obtain formulas for solutions of rational difference equations such as xn+1=1±xn−1yn/1−yn,yn+1=1±yn−1xn/1−xn, and xn+1=1±xn−1yn−2/1−yn,yn+1=1±yn−1xn−2/1−xn, where the initial conditions x−2, x−1, x0, y−2, y−1, y0 are non-zero ...
Khalil S. Al-Basyouni, Elsayed M. Elsayed   +1 more
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