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)expa(k)-b(k)x(k)-p(k,x(k),y(k),x(k-μ),y(k-ν))y(k)x(k),y(k+1)=y(k)expc(k)-d(k)y(k)x(k-μ),where μ, ν 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.