On the Rational Recursive Sequence xn+1=(α-βxn)/(γ-δxn-xn-k)

We study the global stability, the periodic character, and the boundedness character of the positive solutions of the difference equation x n+1 = (a -βx n )/(γ - δx n - x n-k ), n = 0,1,2,..., k ∈ {1,2,...}, in the two cases: (i) 6 > 0, α > 0, y > p > 0; (ii) 6 > 0, a = 0, γ,β > 0, where the coefficients a, β, y, and 6, and the initial conditions x-k, x-k+1,..., x -1 , x 0 are real numbers. We show that the positive equilibrium of this equation is a global attractor with a basin that depends on certain conditions posed on the coefficients of this equation.