Global behavior of a discrete population model

In this work, the global behavior of a discrete population model {x(n+1) =alpha x(n)e(-yn) +beta, y(n+1) =alpha x(n)(1 - e(-y)n) , n=0, 1,2, . . . , is considered, where alpha is an element of (0, 1), beta is an element of (0, +infinity), and the initial value (x(0), y(0)) is an element of [0, infinity) x [0, infinity). To illustrate the dynamics behavior of this model, the boundedness, periodic character, local stability, bifurcation, and the global asymptotic stability of the solutions are investigated.