Global attractivity and convergence to a two-cycle in a difference equation

We obtain conditions under which every positive solution of a difference equation of the form y n+1=y n-1 f(y n-1, y n ), n=0, 1, 2, … is attracted to its positive equilibrium. We also obtain conditions under which every positive solution approaches a two-cycle, which may be an equilibrium. The results apply to a population model with two age classes