In this paper, we consider a system whose state x changes to [image omitted] if a perturbation occurs at the time t, for [image omitted] and the state x changes to the new state [image omitted] at the time t, for [image omitted] . Here, [image omitted] and [image omitted] are logistic maps. We assume that the number of perturbations in the interval [image omitted] is a discrete random variable [image omitted] . We show that under certain conditions on the parameters [image omitted] and [image omitted] , the system has, even for the non-contractive case, an unique stationary probability measure, the support of which can be either a Cantor set or an interval.