Starvation kinetics of oscillating microbial populations

We study the dynamics of a model which is perhaps the simplest one which describes the competition between different classes of bacteria competing for the same resource. The competition is not entirely antagonistic but is partly syntrophic, resulting in a model which has aspects of activator-inhibitor kinetics, and which exhibits oscillations. In conditions of starvation, these oscillations are extreme, resulting in boom-and-bust dynamics in which there are concentrated population spikes interspersed by extremely low population levels. In practice, continuous models become inappropriate at such low levels, and a stochastic generalisation allows the possibility of extinction. We explain why these results occur, and we give an asymptotic and numerical description of the resulting dynamics of the solutions. This description is likely to be generally applicable to systems exhibiting autocatalytic oscillation, and we suggest that for a larger number of such interacting populations, the solutions may exhibit multiple spiking events.