Weakly coupled traveling waves for a model of growth and competition in a flow reactor
For a reaction-diffusion model of microbial flow reactor with twocompeting populations, we show the coexistence of weakly coupled travelingwave solutions in the sense that one organism undergoes a population growthwhile another organism remains in a very low population density in the firsthalf inter...
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| Format: | Article |
| Language: | English |
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AIMS Press
2005-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.79 |
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| author | Wenzhang Huang |
| author_facet | Wenzhang Huang |
| author_sort | Wenzhang Huang |
| collection | DOAJ |
| description | For a reaction-diffusion model of microbial flow reactor with twocompeting populations, we show the coexistence of weakly coupled travelingwave solutions in the sense that one organism undergoes a population growthwhile another organism remains in a very low population density in the firsthalf interval of the space line; the population densities then exchange theposition in the next half interval. This type of traveling wave can occur onlyif the input nutrient slightly exceeds the maximum carrying capacity for thesetwo populations. This means, lacking an adequate nutrient, two competingorganisms will manage to survive in a more economical way. |
| format | Article |
| id | doaj-art-f13c4b573a6447f8825120c06f1dfd4a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f13c4b573a6447f8825120c06f1dfd4a2025-01-24T01:51:11ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-10-0131798710.3934/mbe.2006.3.79Weakly coupled traveling waves for a model of growth and competition in a flow reactorWenzhang Huang0Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899For a reaction-diffusion model of microbial flow reactor with twocompeting populations, we show the coexistence of weakly coupled travelingwave solutions in the sense that one organism undergoes a population growthwhile another organism remains in a very low population density in the firsthalf interval of the space line; the population densities then exchange theposition in the next half interval. This type of traveling wave can occur onlyif the input nutrient slightly exceeds the maximum carrying capacity for thesetwo populations. This means, lacking an adequate nutrient, two competingorganisms will manage to survive in a more economical way.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.79microbial flow reactor modelunstable manifoldreaction-diffusion equationsweakly coupled traveling waves. |
| spellingShingle | Wenzhang Huang Weakly coupled traveling waves for a model of growth and competition in a flow reactor Mathematical Biosciences and Engineering microbial flow reactor model unstable manifold reaction-diffusion equations weakly coupled traveling waves. |
| title | Weakly coupled traveling waves for a model of growth and competition in a flow reactor |
| title_full | Weakly coupled traveling waves for a model of growth and competition in a flow reactor |
| title_fullStr | Weakly coupled traveling waves for a model of growth and competition in a flow reactor |
| title_full_unstemmed | Weakly coupled traveling waves for a model of growth and competition in a flow reactor |
| title_short | Weakly coupled traveling waves for a model of growth and competition in a flow reactor |
| title_sort | weakly coupled traveling waves for a model of growth and competition in a flow reactor |
| topic | microbial flow reactor model unstable manifold reaction-diffusion equations weakly coupled traveling waves. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.79 |
| work_keys_str_mv | AT wenzhanghuang weaklycoupledtravelingwavesforamodelofgrowthandcompetitioninaflowreactor |