Oscillation and asymptotic behavior of a class of higher order nonlinear recursive sequences

We investigate the global attractivity, the periodic behavior, and the invariant interval with the semicycles character of solutions of the equation x n + 1 = α + γ x n - 2 k + 1 Bx n - k + 1 + Cx n - 2 k + 1 , n = 0 , 1 , 2 , … for all admissible non-negative values of the parameters α , γ , B , C and the initial conditions x −2 k +1 ,… , x 1 , x 0 . We show that the solutions exhibit a periodic attitude depending on the parameters of the family of the above mentioned difference equation in comparison with each other.