  A R\"ossler model perturbed with a piecewise constant function is
investigated. The perturbation function used in the model is constructed by
means of the logistic map. In the absence of the perturbation the system is
assumed to possess two equilibrium points one of which is linearly stable. The
occurrences of period-doubling cascade and intermittency are numerically
investigated. Extensions of the aforementioned phenomena among coupled
R\"ossler systems are also shown. Our results reveal that discontinuous
perturbations are capable of generating continuous chaos.
