Naimark-Sacker bifurcation of second order rational difference equation with quadratic terms

We investigate the global asymptotic stability and Naimark-Sacker bifurcation of the difference equation xn+1 = \frac{F}{bxnxn-1 + cx2n-1 + f} n = 0, 1, . . . ,with non-negative parameters and nonnegative initial conditions x-1, x0 such that bx0x-1 + cx² -1 + f 0. By using fixed point theorem for monotone maps we find the region of parameters where the unique equilibrium is globally asymptotically stable.