Chaotic dynamics in predator-prey models with time delay

First we will consider the dynamics of one of the simplest classical predator-prey models and then incorporate a delay to model the time between the capture of the prey and its conversion to viable biomass. Considering the time delay introduces a sequence of period doubling bifurcations eventually leading to chaos, with a strange attractor that resembles the chaotic attractor of the Mackey-Glass equation. We will then compare the dynamics with that of the analogous models for predator-prey dynamics in the chemostat, a device for the continuous culture of microorganisms.