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

  • Received: 01 March 2005 Accepted: 29 June 2018 Published: 01 November 2005
  • MSC : 34D20, 34D23, 92D30.

  • 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.

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

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  • 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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  • © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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