Global stability in difference equations satisfying the generalized Yorke condition

We present several conditions sufficient for global stability of the zero solution of nonautonomous difference equation xn+1 = qxn + fn(xn, . . ., xn−k ), n ∈ Z, when the nonlinearities fn satisfy a sort of negative feedback condition. Moreover, for every k ∈ N, we indicate qk such that one of our stability conditions is sharp if q ∈ (0,qk ]. We apply our results to discrete versions of Nicholson’s blowflies equation, the Mackey–Glass equations, and the Wazewska and Lasota equation.  2004 Elsevier Inc. All rights reserved.