scholarly journals On the System of High Order Rational Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Qianhong Zhang ◽  
Wenzhuan Zhang ◽  
Yuanfu Shao ◽  
Jingzhong Liu
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solution ◽  
Difference Equations ◽  
High Order ◽  
Rational Difference Equations

This paper is concerned with the boundedness, persistence, and global asymptotic behavior of positive solution for a system of two rational difference equations xn+1=A+(xn/∑i=1kyn-i),    yn+1=B+(yn/∑i=1kxn-i),  n=0,1,…,k∈{1,2,…}, where A,B∈0,∞,  x-i∈0,∞, and   y-i∈0,∞,  i=0,1,2,…,k.

scholarly journals Dynamical Behavior of a System of Third-Order Rational Difference Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Qianhong Zhang ◽  
Jingzhong Liu ◽  
Zhenguo Luo
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Positive Solution ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Dynamical Behavior ◽  
Third Order ◽  
Rational Difference Equations ◽  
Rational Difference Equation

This paper deals with the boundedness, persistence, and global asymptotic stability of positive solution for a system of third-order rational difference equationsxn+1=A+xn/yn-1yn-2,yn+1=A+yn/xn-1xn-2,n=0,1,…, whereA∈(0,∞),x-i∈(0,∞);y-i∈(0,∞),i=0,1,2. Some examples are given to demonstrate the effectiveness of the results obtained.

scholarly journals Global Attractor of Solutions of a Rational System in the Plane

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Miron B. Bekker ◽  
Martin J. Bohner ◽  
Hristo D. Voulov
Keyword(s):  
Positive Solution ◽  
Global Attractor ◽  
Difference Equations ◽  
Autonomous System ◽  
Additional Assumption ◽  
Finite Limit ◽  
Two Dimensional ◽  
Rational System ◽  
Rational Difference Equations

We consider a two-dimensional autonomous system of rational difference equations with three positive parameters. It was conjectured that every positive solution of this system converges to a finite limit. Here we confirm this conjecture, subject to an additional assumption.

scholarly journals On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers

2019 ◽  
Author(s):  
İnci Okumuş ◽  
Yüksel Soykan
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Rational Difference Equations ◽  
Tribonacci Numbers

In this study, we investigate the form of solutions, stability character and asymptotic behavior of the following four rational difference equations x_{n+1} = (1/(x_{n}(x_{n-1}±1)±1)), x_{n+1} = ((-1)/(x_{n}(x_{n-1}±1)∓1)), such that their solutions are associated with Tribonacci numbers.

On the system of high order rational difference equations

2005 ◽  
Vol 171 (2) ◽  
pp. 853-856 ◽  
Author(s):  
Xiaofan Yang ◽  
Yaoxin Liu ◽  
Sen Bai
Keyword(s):  
Difference Equations ◽  
High Order ◽  
Rational Difference Equations

On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers

2020 ◽  
Vol 70 (3) ◽  
pp. 641-656
Author(s):  
Amira Khelifa ◽  
Yacine Halim ◽  
Abderrahmane Bouchair ◽  
Massaoud Berkal
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
Fibonacci Numbers ◽  
Higher Order ◽  
Real Numbers ◽  
Lucas Numbers ◽  
Rational Difference Equations ◽  
Initial Values ◽  
Fibonacci And Lucas Numbers

AbstractIn this paper we give some theoretical explanations related to the representation for the general solution of the system of the higher-order rational difference equations$$\begin{array}{} \displaystyle x_{n+1} = \dfrac{1+2y_{n-k}}{3+y_{n-k}},\qquad y_{n+1} = \dfrac{1+2z_{n-k}}{3+z_{n-k}},\qquad z_{n+1} = \dfrac{1+2x_{n-k}}{3+x_{n-k}}, \end{array}$$where n, k∈ ℕ0, the initial values x−k, x−k+1, …, x0, y−k, y−k+1, …, y0, z−k, z−k+1, …, z1 and z0 are arbitrary real numbers do not equal −3. This system can be solved in a closed-form and we will see that the solutions are expressed using the famous Fibonacci and Lucas numbers.

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