The effect of periodicity in maps

Autonomous discrete maps with equilibria are subjected to 2-periodic forcing and the averages of the resulting 2-cycle solutions are compared to the equilibrium values of the associated autonomous equation. Conditions under which the averages of the 2-cycles are larger (smaller) than the equilibria are derived for 1-dimensional maps near bifurcation points and also for small amplitude forcing. Discrete systems of a particular form (motivated by models in population biology) are also studied by means of perturbations along contours of the average solution surface.