scholarly journals Asymptotic Behavior of some Rational Difference Equations

2016 ◽  
Vol 136 (8) ◽  
pp. 18-24
Author(s):  
E.M. Elabbasy ◽  
A.A. El-Biaty
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Rational Difference Equations

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 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 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.

Sign in / Sign up

Export Citation Format

Share Document