Basins of Attraction of Certain Homogeneous Second Order Quadratic Fractional Difference Equation M. Gari´ c-Demirovi´ c Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina M. R. S. Kulenovi´ c * Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881-0816, USA, M. Nurkanovi´ c Department of Mathematics, University of Tuzla, 75 000 Tuzla, Bosnia and Herzegovina August 31, 2013 Abstract We investigate the basins of attraction of equilibrium points and period-two solution of the difference equation of the form x n+1 = Bx n x n-1 + Cx 2 n-1 ax 2 n + bx n x n-1 , n =0, 1,..., where the parameters a, b, C, B are positive numbers and the initial conditions x -1 ,x 0 are arbitrary nonnegative numbers. We show that this equation exhibits global period-two bifurcation, as certain parameters are pasing through the critical value. Keywords: attractivity, basin, difference equation, invariant sets, periodic solutions, stable set AMS 2000 Mathematics Subject Classification: 39A10, 39A11 * Corresponding author