PERIODIC ROTATING WAVES
IN A MODEL OF MICROBIAL COMPETITION
IN A CIRCULAR GRADOSTAT

HAL L. SMITH

Abstract. Periodic rotating waves of discrete type (ponies on a merry-go-round) are shown to exist for a mathematical model of competition between two microbial populations for a single nutrient in a circularly configured array of n vessels, a gradostat, in response to a periodic rotating wave of nutrient concentration in the reservoirs feeding the vessels of the gradostat. These periodic rotating waves of nutrient and microbial population concentrations represent coexistence of the two populations. For gradostats consisting of a moderate to a large number n of vessels, the rotating wave solutions are approximated by passage to the continuum limit (n → ∞). This allows replacing a large periodic system of ordinary differential equations by a periodic reaction-diffusion system on the circle. Rotating wave solutions of this system are approximated by a singular perturbation analysis.