Traveling Waves and Weakly Coupled Traveling Waves for a model of Growth and Competition in a Flow Reactor

Dr. Wenzhang Haung

Department of Mathematical Sciences
University of Alabama in Huntsville

October 28, 2005
202 Madison Hall
3:30 PM (Coffee and Cookies at 3:00)

Abstract

For a reaction-diffusion model of microbial flow reactor with two competing populations, we use the unstable manifold theorem, combining with the shooting method and continuous argument, to show the coexistence of traveling wave solutions. In addition, by a bifurcation method we show the existence of weakly coupled traveling wave solutions in the sense that one organism undergoes a population growth while another organism remains in a very low population density in the first half interval of the space line; the population densities then exchange the position in the next half interval. This type of traveling wave can occur only if the input nutrient slightly exceeds the "minimum carrying capacity for these two populations" This indicates that, in the lack of adequate nutrient, two competing organism will manage to survive in a more "economical" way -- an interesting phenomenon.