This study investigates the effects of periodic perturbations on the dynamics of competition between plasmid-bearing and plasmid-free cells in recombinant DNA cultures. The model used in this numerical investigation was shown in a number of studies to be able to predict the occurrence of periodic behavior for selected growth rates of the competing populations. This research investigates the different dynamic behavior predicted by the model when the bioreactor feed conditions are periodically varied. The results show that periodic perturbations can give rise to complex dynamics that include quasi-periodic and period adding bifurcations. The effects of these parametric perturbations on the performance of the competition are also investigated. It is shown that the efficiency of the bioreactor can be substantially improved by an appropriate selection of the forcing amplitude. The effects of the position of the center of forcing on the nature of the emerging dynamic patterns are also investigated.