Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Asymptotic Stability of xn+1-a2xn-1+bxn-k = 0

  • Niamsup, Piyapong (Department of Mathematics, Faculty of Science, Chiangmai University) ;
  • Lenbury, Yongwimon (Department of Mathematics, Faculty of Science, Mahidol University)
  • Received : 2004.07.12
  • Published : 2008.06.30
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Abstract

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

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References

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