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On the asymptotic stability of xn+1=(a+xnxn-k)/(xn+xn-k)
Journal article   Open access  Peer reviewed

On the asymptotic stability of xn+1=(a+xnxn-k)/(xn+xn-k)

R. Abu-Saris, C. Cinar and I. Yalcinkaya
Computers & mathematics with applications (1987), Vol.56(5), pp.1172-1175
01/09/2008
DOI: https://doi.org/10.1016/j.camwa.2008.02.028

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We prove that the equilibrium solution of the rational difference equation x(n)+1 = (a + x(n)x(n-k))/(x(n) + x(n-k)), n = 0, 1, 2, ... where k is a nonnegative integer, a >= 0, and x(-k), x(0) > 0, is globally asymptotically stable. (c) 2008 Elsevier Ltd. All rights reserved.
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https://doi.org/10.1016/j.camwa.2008.02.028View
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