scholarly journals Global asymptotic stability in a perturbed higher-order linear difference equation

2003 ◽  
Vol 45 (6-9) ◽  
pp. 1195-1202 ◽  
Author(s):  
M. Pituk
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Global Asymptotic Stability ◽  
Linear Difference Equation ◽  
Higher Order ◽  
Order Linear

scholarly journals On the Dynamics of a Higher-Order Rational Difference Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
A. M. Ahmed
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Global Asymptotic Stability ◽  
Higher Order ◽  
Real Numbers ◽  
Rational Difference Equation

The aim of this paper is to investigate the global asymptotic stability and the periodic character for the rational difference equationxn+1=αxn-1/(β+γΠi=lkxn-2ipi),  n=0,1,2,…, where the parametersα,β,γ,pl,pl+1,…,pkare nonnegative real numbers, andl,kare nonnegative integers such thatl≤k.

scholarly journals Global Behavior of a New Rational Nonlinear Higher-Order Difference Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-4 ◽  
Author(s):  
Wen-Xiu Ma
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Global Asymptotic Stability ◽  
Nonnegative Integer ◽  
Equilibrium Solution ◽  
Higher Order ◽  
Positive Equilibrium ◽  
Global Behavior ◽  
Order Difference ◽  
Order Difference Equation

Let k be a nonnegative integer and c a real number greater than or equal to 1. We present qualitative global behavior of solutions to a rational nonlinear higher-order difference equation zn+1=(czn+zn-k+c-1znzn-k)/(znzn-k+c),  n≥0, with positive initial values z-k,z-k+1,⋯,z0, and show the global asymptotic stability of its positive equilibrium solution.

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