Global stability in difference equations satisfying the generalized Yorke condition

Abstract

We present several conditions sufficient for global stability of the zero solution of nonautonomous difference equation x(n+1) qx(n) + f(n) (x(n),..., x(n-k)), n is an element of Z, when the nonlinearities f(n) satisfy a sort of negative feedback condition. Moreover, for every k is an element of N, we indicate q(k) such that one of our stability conditions is sharp if q is an element of (0, q(k)]. We apply our results to discrete versions of Nicholson's blowflies equation, the Mackey-Glass equations, and the Wazewska and Lasota equation.