Previous results of a periodically perturbed Oregonator have shown synchronized periods and patterns composed of large and small oscillations. Next amplitude maps of the small oscillations show the existence of three-branch return maps. A family of maps consisting of three branches was constructed in order to mimic the behavior of the results of the differential equations. These little known maps show clearly the behavior of the perturbed system, The maps as well as the real system do not have any chaotic motions and mainly have periodic ones.