Publication:
The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0

Issued Date

2008-01-01

Resource Type

Article

ISSN

12256951

DOI

10.5666/KMJ.2008.48.2.173

Other identifier(s)

2-s2.0-77952124402

Rights

Mahidol University

Rights Holder(s)

SCOPUS

Bibliographic Citation

Kyungpook Mathematical Journal. Vol.48, No.2 (2008), 173-181

Suggested Citation

Piyapong Niamsup, Yongwimon Lenbury The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0. Kyungpook Mathematical Journal. Vol.48, No.2 (2008), 173-181. doi:10.5666/KMJ.2008.48.2.173 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/19423

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Title

The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0

Author(s)

Piyapong Niamsup
 Yongwimon Lenbury

Other Contributor(s)

Chiang Mai University
 Mahidol University

Abstract

We give the necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation xn+1-a2xn-1+bxn-k= 0, 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.

Keyword(s)

Mathematics

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https://repository.li.mahidol.ac.th/handle/20.500.14594/19423

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Scopus 2006-2010