The effect of periodicity in maps

Autonomous discrete maps with equilibria are subjected to 2-periodic forcin g and the averages of the resulting 2-cycle solutions are compared to the e quilibrium values of the associated autonomous equation. Conditions under w hich the averages of the 2-cycles are larger (smaller) than the equilibria are derived for 1-dimensional maps near bifurcation points and also for sma ll amplitude forcing. Discrete systems of a particular form (motivated by m odels in population biology) are also studied by means of perturbations alo ng contours of the average solution surface.