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

Piyapong NiamsupYongwimon LenburyChiang Mai UniversityMahidol University2018-07-122018-07-122008-01-01Kyungpook Mathematical Journal. Vol.48, No.2 (2008), 173-181122569512-s2.0-77952124402https://repository.li.mahidol.ac.th/handle/20.500.14594/19423We 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.Mahidol UniversityMathematicsThe asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0ArticleSCOPUS10.5666/KMJ.2008.48.2.173