I will discuss my recent work with Mikko Stenlund on periodic pulsatile perturbations of flows that admit weakly stable hyperbolic limit cycles. We study the time-T maps induced by the perturbed flows. We formulate computable conditions that imply the existence of SRB measures with strong stochastic properties for a set of values of T of positive Lebesgue measure. This is an example of shear-induced chaos: the existence of shear in the unperturbed flow can cause sustained, observable chaos to replace a stable dynamical structure when the system is forced with a periodic pulsatile drive.