Global stability of a population model

In this paper, we study the qualitative behavior of a discrete-time population model. More precisely, we investigate boundedness character, existence and uniqueness of positive equilibrium point, local asymptotic stability and global asymptotic stability of unique positive equilibrium point, and the rate of convergence of positive solutions of a population model. In particular, our results solve an open problem proposed by Kulenvić and Ladas in their monograph (Kulenvić and Ladas, 2002) [8]. Some numerical examples are given to verify our theoretical results.