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The Asymptotic Stability of xn+1-a2xn-1+bxn-k = 0
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  • 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;
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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.
the asymptotic stability;linear delay difference equation;
 Cited by
C. W. Clark, A delay-recruitment model of population dynamics, with an application to baleen whale populations, J.Math. Biol., 3 (1976), 381-391. crossref(new window)

S. A. Kuruklis, The asymptotic stability of $x_{n+1} − ax_n + bx_{n−k} = 0$, J. Math. Anal. Appl., 188 (1994), 719-731. crossref(new window)

S. A. Levin and R. M. May, A note on difference-delay equations, Theoret. Popul. Biol., 9 (1976), 178-187. crossref(new window)