Dynamics of nonlinear difference equation

The main goal of this paper is to investigate the boundedness, invariant intervals, semi-cycles and global attractivity of all nonnegative solutions of the equation xn+1 = βxn + γ xn−k A + Bxn + C xn−k , n ∈ N0, where the parameters β, γ, A, B and C and the initial conditions x−k , x−k+1,..., x0 are non-negative real numbers, k = {1, 2,...}. We give a detailed description of the semi-cycles of solutions, and determine conditions that satisfy the global asymptotic stability of the equilibrium point