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

1. Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899

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.
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Keywords Microbial flow reactor model; unstable manifold; reaction-diffusion equations; weakly coupled traveling waves.

Citation: Wenzhang Huang. Weakly coupled traveling waves for a model of growth and competition in a flow reactor. Mathematical Biosciences and Engineering, 2006, 3(1): 79-87. doi: 10.3934/mbe.2006.3.79

 

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Copyright Info: 2006, Wenzhang Huang, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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