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Mathematical Biosciences and Engineering

2019, Volume 16, Issue 1: 205-221. doi: 10.3934/mbe.2019011
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Mathematical analysis of a chemostat system modeling the competition for light and inorganic carbon with internal storage

  • 1.
    Department of Natural Science in the Center for General Education, Chang Gung University, Guishan, Taoyuan 333, Taiwan
  • 2.
    Community Medicine Research Center, Chang Gung Memorial Hospital, Keelung, Keelung 204, Taiwan
  • Received: 17 April 2018 Accepted: 19 October 2018 Published: 11 December 2018

  • This paper investigates a mathematical model of competition between two species for inorganic carbon and light in a well-mixed water column. The population growth of the species depends on the consumption of two substitutable forms of inorganic carbon, "CO2" (dissolved CO2 and carbonic acid) and "CARB" (bicarbonate and carbonate ions), which are stored internally. Besides, uptake rates also includes self-shading by the phytoplankton population, that is, an increase in population density will reduce light available for photosynthesis, and thereby reducing further carbon assimilation and population growth. We also incorporate the fact that carbon is lost by respiration, and the respiration rate is assumed to be proportional to the size of the transient carbon pool. Then we study the extinction and persistence of a single-species system. Finally, we show that coexistence of the two-species system is possible, depending on parameter values, and both persistence of one population.

    Citation: Fu-Yuan Tsai, Feng-BinWang. Mathematical analysis of a chemostat system modeling the competition for light and inorganic carbon with internal storage[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 205-221. doi: 10.3934/mbe.2019011

    Related Papers:

  • This paper investigates a mathematical model of competition between two species for inorganic carbon and light in a well-mixed water column. The population growth of the species depends on the consumption of two substitutable forms of inorganic carbon, "CO2" (dissolved CO2 and carbonic acid) and "CARB" (bicarbonate and carbonate ions), which are stored internally. Besides, uptake rates also includes self-shading by the phytoplankton population, that is, an increase in population density will reduce light available for photosynthesis, and thereby reducing further carbon assimilation and population growth. We also incorporate the fact that carbon is lost by respiration, and the respiration rate is assumed to be proportional to the size of the transient carbon pool. Then we study the extinction and persistence of a single-species system. Finally, we show that coexistence of the two-species system is possible, depending on parameter values, and both persistence of one population.


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  • © 2019 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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