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Single species growth consuming inorganic carbon with internal storage in a poorly mixed habitat

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Abstract

This paper presents a PDE system modeling the growth of a single species population consuming inorganic carbon that is stored internally in a poorly mixed habitat. Inorganic carbon takes the forms of “CO2” (dissolved CO2 and carbonic acid) and “CARB” (bicarbonate and carbonate ions), which are substitutable in their effects on algal growth. We first establish a threshold type result on the extinction/persistence of the species in terms of the sign of a principal eigenvalue associated with a nonlinear eigenvalue problem. If the habitat is the unstirred chemostat, we add biologically relevant assumptions on the uptake functions and prove the uniqueness and global attractivity of the positive steady state when the species persists.

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Acknowledgements

We are grateful to three anonymous referees for their careful reading and helpful suggestions which led to improvements of our original manuscript. We also express our thanks to Prof. H. R. Thieme for suggesting us the key reference Mallet-Paret and Nussbaum (2010) in this paper.

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Authors and Affiliations

  1. Department of Mathematics, National Tsing Hua University, Hsinchu, 300, Taiwan

    Sze-Bi Hsu

  2. Department of Mathematics, The Ohio State University, Columbus, OH, USA

    King-Yeung Lam

  3. Department of Natural Science in the Center for General Education, Chang Gung University, Guishan, Taoyuan, 333, Taiwan

    Feng-Bin Wang

  4. Community Medicine Research Center, Chang Gung Memorial Hospital, Keelung, Keelung, 204, Taiwan

    Feng-Bin Wang

Authors
  1. Sze-Bi Hsu
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  2. King-Yeung Lam
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  3. Feng-Bin Wang
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Corresponding author

Correspondence to Feng-Bin Wang.

Additional information

Sze-Bi Hsu: Research supported in part by Ministry of Science and Technology, Taiwan.

King-Yeung Lam: Research partially supported by NSF Grant DMS-1411476.

Feng-Bin Wang: Research supported in part by Ministry of Science and Technology, Taiwan; and National Center for Theoretical Sciences (NCTS), National Taiwan University; and Chang Gung Memorial Hospital (BMRPD18 and NMRPD5F0541).

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Hsu, SB., Lam, KY. & Wang, FB. Single species growth consuming inorganic carbon with internal storage in a poorly mixed habitat. J. Math. Biol. 75, 1775–1825 (2017). https://doi.org/10.1007/s00285-017-1134-5

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  • DOI: https://doi.org/10.1007/s00285-017-1134-5

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