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 equationxn+1=α+γxn-2k+1Bxn-k+1+Cxn-2k+1,n=0,1,2,…for all admissible non-negative values of the parameters α, γ, B, C and the initial conditions x−2k+1 ,… , x1, x0. 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.