title: Global dynamics of certain homogeneous second-order quadratic fractional difference equation.
abstract: We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x(n+1) = x²(n-1)/(ax²(n) + bx(n)x(n-1) + cx²(n-1)), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x₋₁ and x₀ 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.
authors.affiliation: Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina.
authors.forename: M
authors.initials: M
authors.lastname: Garić-Demirović
authors.affiliation: Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA.
authors.forename: M R S
authors.initials: MR
authors.lastname: Kulenović
authors.affiliation: Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina.
authors.forename: M
authors.initials: M
authors.lastname: Nurkanović
mesh_terms: D008433:Mathematics