Global asymptotic stability for a higher order nonlinear rational difference equations

2006 ◽  
Vol 182 (2) ◽  
pp. 1819-1831 ◽  
Author(s):  
Xing-Xue Yan ◽  
Wan-Tong Li ◽  
Zhu Zhao
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Higher Order ◽  
Rational Difference Equations

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 ASYMPTOTIC STABILITY FOR GENERAL SYMMETRIC RATIONAL DIFFERENCE EQUATIONS

2009 ◽  
Vol 81 (2) ◽  
pp. 251-259 ◽  
Author(s):  
CONG ZHANG ◽  
HONG-XU LI ◽  
NAN-JING HUANG
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Global Attractivity ◽  
Positive Equilibrium ◽  
Globally Asymptotically Stable ◽  
Rational Difference Equations ◽  
Rational Difference Equation ◽  
Special Case ◽  
Appl Math

AbstractWe investigate the global asymptotic stability for positive solutions to a class of general symmetric rational difference equations and prove that the unique positive equilibrium 1 of the general symmetric rational difference equations is globally asymptotically stable. As a special case of our result, we solve the conjecture raised by Berenhaut, Foley and Stević [‘The global attractivity of the rational difference equationyn=(yn−k+yn−m)/(1+yn−kyn−m)’,Appl. Math. Lett.20(2007), 54–58].

scholarly journals Global Behavior of Two Families of Nonlinear Symmetric Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Wanping Liu ◽  
Xiaofan Yang ◽  
Luxing Yang
Keyword(s):  
Asymptotic Stability ◽  
Recent Result ◽  
Positive Solutions ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Exponential Convergence ◽  
Higher Order ◽  
The Other ◽  
Global Behavior ◽  
Order Difference

We mainly investigate the global asymptotic stability and exponential convergence of positive solutions to two families of higher-order difference equations, one of which was recently studied in Stević's paper (2010). A new concise proof is given to a quite recent result by Stević and analogous parallel result of the other inverse equation, which extend related results of Aloqeili (2009), Berenhaut and Stević (2007), and Liao et al. (2009).

scholarly journals A New Part-Metric-Related Inequality Chain and an Application

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaofan Yang ◽  
Fangkuan Sun ◽  
Yuan Yan Tang
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Rational Difference Equations ◽  
Related Inequality

Part-metric-related (PMR) inequality chains are elegant and are useful in the study of difference equations. In this paper, we establish a new PMR inequality chain, which is then applied to show the global asymptotic stability of a class of rational difference equations.

scholarly journals Dynamics of a System of Higher Order Difference Equations with Quadratic Terms

2021 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Asymptotic Stability ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Higher Order ◽  
Related System ◽  
Order Difference ◽  
Initial Values

In this paper we investigate the global asymptotic stability of following system ofhigher order difference equations with quadratic terms:xn+1=A+Byn/yn−m^2, yn+1=A+Bxn/xn−m^2, where A and B are positive numbers and the initial values are positive numbers.We also study the boundedness, rate of convergence and oscillation behaviour of thesolutions of related system.

scholarly journals Dynamics of System of Higher Order Difference Equations with Quadratic Terms

2020 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Asymptotic Stability ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Higher Order ◽  
Related System ◽  
Order Difference ◽  
Initial Values

This paper aims to investigate the global asymptotic stability of following system of higher order difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-m}²)),y_{n+1}=A+B((x_{n})/(x_{n-m}²)) where A and B are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system.

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