Global stability of y(n+1)=p+qy(n)+ry(n-k)/1+y(n)

摘要

In this paper, we investigate the global stability of difference equation, y(n+1) = p+qy(n)+ry(n-k)/1+y(n), n = 0, 1, 2,..., where the initial conditions y(-k), . . . , y(-1), y(0) are non-negative, k is an element of{1, 2, 3,... }, and the parameters p, q and r are non-negative. We show that when r < q + 1, then the unique positive equilibrium of this equation is globally asymptotically stable and when r > q + 1, and k is odd.. then this equation possesses unbounded solutions. (c) 2006 Elsevier Inc. All rights reserved.