Abstract

Continuing our previous investigations, we give simple sufficient conditions for the global stability of the zero solution of the difference equation x n+1 = qx n + n(x n x n-k), n, where the nonlinear functions n satisfy the Yorke condition. For every positive integer k, we represent the interval (0, 1] as the union of [(2k + 2)/3] disjoint subintervals, and, for q from each subinterval, we present a global-stability condition in explicit form. The conditions obtained are sharp for the class of equations satisfying the Yorke condition. © 2008 Springer Science+Business Media, Inc.