American Institute of Mathematical Sciences

Advanced
2006, 3(1): 79-87. doi: 10.3934/mbe.2006.3.79

Weakly coupled traveling waves for a model of growth and competition in a flow reactor

Wenzhang Huang 1,

1. 

Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, United States

Received  March 2005 Revised  April 2005 Published  November 2005

For a reaction-diffusion model of microbial flow reactor with two competing populations, we show the coexistence 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 maximum carrying capacity for these two populations. This means, lacking an adequate nutrient, two competing organisms will manage to survive in a more economical way.
Keywords: Microbial flow reactor model, unstable manifold, reaction-diffusion equations, weakly coupled traveling waves..
Mathematics Subject Classification: 34D20, 34D23, 92D3.
Citation: Wenzhang Huang. Weakly coupled traveling waves for a model of growth and competition in a flow reactor. Mathematical Biosciences & Engineering, 2006, 3 (1) : 79-87. doi: 10.3934/mbe.2006.3.79
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