Global asymptotic stability for nonlinear difference equations

2006 ◽  
Vol 182 (1) ◽  
pp. 67-72 ◽  
Author(s):  
Yuehui Peng
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Nonlinear Difference Equations

Dynamical behavior of a P-dimensional system of nonlinear difference equations

2021 ◽  
Vol 71 (4) ◽  
pp. 903-924
Author(s):  
Yacine Halim ◽  
Asma Allam ◽  
Zineb Bengueraichi
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Positive Equilibrium ◽  
Dimensional System ◽  
Nonlinear Difference Equations

Abstract In this paper, we study the periodicity, the boundedness of the solutions, and the global asymptotic stability of the positive equilibrium of the system of p nonlinear difference equations x n + 1 ( 1 ) = A + x n − 1 ( 1 ) x n ( p ) , x n + 1 ( 2 ) = A + x n − 1 ( 2 ) x n ( p ) , … , x n + 1 ( p − 1 ) = A + x n − 1 ( p − 1 ) x n ( p ) , x n + 1 ( p ) = A + x n − 1 ( p ) x n ( p − 1 ) $$\begin{equation*}x^{(1)}_{n+1}=A+\dfrac{x^{(1)}_{n-1}}{x^{(p)}_{n}},\quad x^{(2)}_{n+1}=A+\dfrac{x^{(2)}_{n-1}}{x^{(p)}_{n}},\quad\ldots,\quad x^{(p-1)}_{n+1}=A+\dfrac{x^{(p-1)}_{n-1}}{x^{(p)}_{n}},\quad x^{(p)}_{n+1}=A+\dfrac{x^{(p)}_{n-1}}{x^{(p-1)}_{n}} \end{equation*} $$ where n ∈ ℕ0, p ≥ 3 is an integer, A ∈ (0, +∞) and the initial conditions x − 1 ( j ) $x_{-1}^{(j)}$ , x 0 ( j ) $x_{0}^{(j)}$ , j = 1, 2, …, p are positive numbers.

scholarly journals Asymptotic Stability for a Class of Nonlinear Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Chang-you Wang ◽  
Shu Wang ◽  
Zhi-wei Wang ◽  
Fei Gong ◽  
Rui-fang Wang
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Initial Conditions ◽  
Real Numbers ◽  
Nonlinear Difference Equations ◽  
Positive Real ◽  
Fractional Difference ◽  
Fractional Difference Equation

We study the global asymptotic stability of the equilibrium point for the fractional difference equationxn+1=(axn-lxn-k)/(α+bxn-s+cxn-t),n=0,1,…, where the initial conditionsx-r,x-r+1,…,x1,x0are arbitrary positive real numbers of the interval(0,α/2a),l,k,s,tare nonnegative integers,r=max⁡⁡{l,k,s,t}andα,a,b,care positive constants. Moreover, some numerical simulations are given to illustrate our results.

scholarly journals Attracting Sets Of Nonlinear Difference Equations With Time-Varying Delays

2018 ◽  
Vol 14 (2) ◽  
pp. 7975-7982
Author(s):  
Danhua He
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Nonlinear Difference Equations ◽  
Halanay Inequality ◽  
Attracting Set

In this paper, a class of nonlinear difference equations with time-varying delays is considered. Based on a generalized discrete Halanay inequality, some sufficient conditions for the attracting set and the global asymptotic stability of the nonlinear difference equations with time-varying delays are obtained.

scholarly journals Global Asymptotic Stability of a Family of Nonlinear Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Maoxin Liao
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Recent Literature ◽  
Nonlinear Difference Equation ◽  
Nonlinear Difference Equations

In this note, we consider global asymptotic stability of the following nonlinear difference equationxn=(∏i=1v(xn-kiβi+1)+∏i=1v(xn-kiβi-1))/(∏i=1v(xn-kiβi+1)-∏i=1v(xn-kiβi-1)),  n=0,1,…, whereki∈ℕ  (i=1,2,…,v),  v≥2,β1∈[-1,1],β2,β3,…,βv∈(-∞,+∞),x-m,x-m+1,…,x-1∈(0,∞), andm=max1≤i≤v{ki}. Our result generalizes the corresponding results in the recent literature and simultaneously conforms to a conjecture in the work by Berenhaut et al. (2007).

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 .

Sign in / Sign up

Export Citation Format

Share Document