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 xn+1=xn-12/(axn2+bxnxn-1+cxn-12),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.