Oscillations in a plasmid turbidostat model with delayed feedback control

A model of competition between plasmid-bearing and plasmid-freeorganisms in a turbidostat with delayed feedback control isinvestigated. By choosing the delay in the measurement of theoptical sensor to the turbidity of the fluid as a bifurcationparameter, we show that Hopf bifurcations can occur as the delaycrosses some critical values. The direction and stability of thebifurcating periodic solutions are determined by the normal formtheory and the center manifold theorem. Computer simulationsillustrate the results.