Competitive exclusion in phytoplankton communities in a eutrophic water column

Robert Stephen Cantrell; King-Yeung Lam

doi:10.3934/dcdsb.2020361

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2021, Volume 26, Issue 4: 1783-1795. Doi: 10.3934/dcdsb.2020361

This issue Previous Article On a stage-structured population model in discrete periodic habitat: III. unimodal growth and delay effect Next Article Traveling wave solutions of a free boundary problem with latent heat effect

Competitive exclusion in phytoplankton communities in a eutrophic water column

Robert Stephen Cantrell^1, and
King-Yeung Lam^2, ,

1.
Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA
2.
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA

^* Corresponding author: K.-Y. Lam
^* Corresponding author: K.-Y. Lam

Received: July 31, 2020

Revised: September 30, 2020

Early access: December 2020

Published: April 2021

RSC is partially supported by NSF grant DMS-1853478; KYL is partially supported by NSF grant DMS-1853561

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Abstract

We analyze a reaction-diffusion system modeling the competition of multiple phytoplankton species which are limited only by light. While the dynamics of a single species has been well studied, the dynamics of the two-species model has only begun to be understood with the recent establishment of a comparison principle. In this paper, we show that the competition of $ N $ similar phytoplankton species, for any number $ N $, generically leads to competitive exclusion. The main tool is the theory of a normalized principal bundle for linear parabolic equations.

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Mathematics Subject Classification: Primary: 35B51, 35K57, 47H07; Secondary: 92D25.

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References

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