Dynamical Behavior of Rational Difference Equation $$x_{n+1}=\frac{x_{n-15}}{\pm 1\pm x_{n-3}x_{n-7}x_{n-11}x_{n-15}}$$

2021 ◽  
Author(s):  
Burak Oğul ◽  
Dağıstan Şimşek ◽  
Abdullah Selçuk Kurbanlı ◽  
Hasan Öğünmez
Keyword(s):  
Difference Equation ◽  
Dynamical Behavior ◽  
Rational Difference Equation

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.

Dynamics of a higher-order rational difference equation

2006 ◽  
Vol 178 (2) ◽  
pp. 345-354 ◽  
Author(s):  
Mehdi Dehghan ◽  
Reza Mazrooei-Sebdani
Keyword(s):  
Difference Equation ◽  
Higher Order ◽  
Rational Difference Equation

scholarly journals Boundedness of solutions and stability of certain second-order difference equation with quadratic term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Emin Bešo ◽  
Senada Kalabušić ◽  
Naida Mujić ◽  
Esmir Pilav
Keyword(s):  
Difference Equation ◽  
Initial Conditions ◽  
Second Order ◽  
Quadratic Term ◽  
Real Numbers ◽  
Positive Real ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Rational Difference Equation

AbstractWe consider the second-order rational difference equation $$ {x_{n+1}=\gamma +\delta \frac{x_{n}}{x^{2}_{n-1}}}, $$xn+1=γ+δxnxn−12, where γ, δ are positive real numbers and the initial conditions $x_{-1}$x−1 and $x_{0}$x0 are positive real numbers. Boundedness along with global attractivity and Neimark–Sacker bifurcation results are established. Furthermore, we give an asymptotic approximation of the invariant curve near the equilibrium point.

scholarly journals Stability of a rational difference equation

2012 ◽  
Vol 25 (12) ◽  
pp. 2232-2239 ◽  
Author(s):  
Qi Wang ◽  
Fanping Zeng ◽  
Xinhe Liu ◽  
Weiling You
Keyword(s):  
Difference Equation ◽  
Rational Difference Equation

scholarly journals Dynamics of a Rational Difference Equation

2010 ◽  
Vol 2010 (1) ◽  
pp. 970720
Author(s):  
Xiu-Mei Jia ◽  
Lin-Xia Hu ◽  
Wan-Tong Li
Keyword(s):  
Difference Equation ◽  
Rational Difference Equation

scholarly journals ON A HIGHER-ORDER RATIONAL DIFFERENCE EQUATION

2016 ◽  
Vol 34 (5_6) ◽  
pp. 369-382 ◽  
Author(s):  
FARIDA BELHANNACHE ◽  
NOURESSADAT TOUAFEK ◽  
RAAFAT ABO-ZEID
Keyword(s):  
Difference Equation ◽  
Higher Order ◽  
Rational Difference Equation
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