Quasi-uniformly asymptotic stability and existence of almost periodic solutions of difference equations with applications in population dynamic systems

In the present paper, we investigate the relationship between the globally quasi-uniformly asymptotic stability and the existence of almost periodic solutions for difference systems. Based on the properties of almost periodic sequences, several criteria are established for the existence of almost periodic solutions for difference systems. Then, some applications in population dynamic systems are presented to illustrate our main results. Finally, we end this paper with some illustrative examples and their numeric simulations. Our results are essentially new and give a method to study the existence of almost periodic solutions of difference equations. The method used in the present paper is much different from that in the literature, and it is the first time that the discrete time Lotka-Volterra systems have been studied by using this method.