The Asymptotic Stability of xn+1-a2xn-1+bxn-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 xn+1-a2xn-1+bxn-k = 0
Niamsup, Piyapong; Lenbury, Yongwimon;

Abstract
We give the necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation $\small{x_{n+1}\;-\;a^2x_{n-1}\;+\;bx_{n-k}\;=\;0}$, n = 0, 1,$\small{\cdots}$, 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
Cited by
References
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