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 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 On the Global Asymptotic Stability of a Second-Order System of Difference Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Ibrahim Yalcinkaya
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
System Of Difference Equations ◽  
Initial Values

A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations where the parameter and the initial values (for .

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