On the asymptotic stability of xn+1=(a+xnxn-k)/(xn+xn-k)
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.
equilibrium solutions rational difference equations global asymptotic stability