The Asymptotic Stability of x_{n+1}-a^{2}x_{n-1}+bx_{n-k} = 0

- Journal title : Kyungpook mathematical journal
- Volume 48, Issue 2, 2008, pp.173-181
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2008.48.2.173

Title & Authors

The Asymptotic Stability of x_{n+1}-a^{2}x_{n-1}+bx_{n-k} = 0

Niamsup, Piyapong; Lenbury, Yongwimon;

Niamsup, Piyapong; Lenbury, Yongwimon;

Abstract

We give the necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation , n = 0, 1,, where a and b are arbitrary real numbers and k is a positive integer greater than 1. The obtained conditions are given in terms of parameters a and b of difference equations. The method of proof is based on arithematic of complex numbers as well as properties of analytic functions.

Keywords

the asymptotic stability;linear delay difference equation;

Language

English

References