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

Abstract

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 - μ ) , y ( k - ν ) ) y ( k ) x ( k ) , y ( k + 1 ) = y ( k ) exp c ( 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.