On the existence and stability of a unique almost periodic sequence solution in discrete predator-prey models with time delays

In this paper, we consider an almost periodic discrete predator-prey models with time delays: {x(k + 1) = x(k) exp {a(k) - b(k)x(k) - p(k, x(k), y(k), x(k - mu), y(k - v)) y(k)/x(k)}, y(k + 1) = y(k) exp {c(k) - d(k)y(k)/x(k-mu)}, where mu, nu are nonnegative integers. Sufficient conditions for the permanence of the system and the existence of a unique uniformly asymptotically stable positive almost periodic sequence solution are obtained by the theory of difference inequality and the work of [S.N. Zhang, G. Zheng, Almost periodic solutions of delay difference systems, Appl. Math. Comput. 131 (2002) 497-516]. The result of this paper is completely new. Some suitable examples are employed to illustrate the feasibility of the main results. (C) 2011 Elsevier Inc. All rights reserved.