Stability analysis of a discrete ecological model.

In this paper, we study the qualitative behavior of following discrete-time population model: x_n+1 = α + βx_n + γx_n-1e^-yn,y_n-1 = δ+ εy_n + ζy_n-1e^-xn, where parameters α,β,γ,δ,ε,ζ and initial conditions x₀, x_-1, y₀,y_-1 are positive real numbers. More precisely, we investigate the existence and uniqueness of positive equilibrium point,boundedness character, persistence, local asymptotic stability, global behavior and rate of convergence of unique positive equilibrium point of this model. Some numerical examples are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]