On the dynamics of the recursive sequence xn+1 = xn−1 β+γ x2n −2xn−4+γ xn−2x2n −4

In this paper, we investigate the global behavior of the difference equation xn+1 = xn−1 β + γ x2 n−2xn−4 + γ xn−2x2n −4 , n = 0, 1, . . . with positive parameters and non-negative initial conditions.