Invasion and Chaos in a Periodically Pulsed Mass-Action Chemostat

This paper contains a simple model for a chemostat with predator, prey, and periodically pulsed substrate. We obtain an exact periodic solution with positive concentrations of substrate and prey. A stability analysis for this solution yields an invasion threshold (the smallest value of the predator′s predation constant consistent with invasion of the chemostat). Above this threshold, there are periodic oscillations in substrate, prey, and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations despite the presence of severe statistical constraints on the behavior of the dependent variables. We determine the average substrate, bacterial, and protozoan concentrations for all periodic orbits, independent of the actual period. We conclude by comparing the behavior of this system with that of two other model chemostats.