Pattern formation and periodical regimes are generally observed for reactive nonlinear chemical systems. They are here obtained for a non-reactive system constituted by an oil (dichloromethane) drop deposited on a surfactant (cetyltrimethylammonium bromide) aqueous solution. The interplay between physicochemical processes (evaporation, solubilization, surfactant adsorption, etc.) and transport phenomena gives rise to a succession of highly organized regimes. Translational motion, pulsations, rotational motion or polygonal shapes are observed as a function of the surfactant concentration. We give here an overview of these behaviours before focusing on the pulsating regime that appears as the periodical expansion and recoil of the drop. In order to obtain a detailed picture of the drop properties at the time the instability starts, the drop shape evolution is studied during the induction period that precedes the beating regime. This evolution is non-trivial and shows the influence of convective flows on the physicochemical processes involved. The large-amplitude regular pulsations are induced by the modification of the surface tension forces applying on the triple contact line, which periodically modifies the spreading properties of the drop.