Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x ( n+1) = x ( n−1) (2)/(ax ( n ) (2) + bx ( n ) x ( n−1) + cx ( n−1) (2)), n = 0,1, 2,…, where the parameters a, b, and c are positive numbers and the initial conditions x (−1) and x (0) are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable.