# American Institute of Mathematical Sciences

April  2021, 26(4): 1783-1795. doi: 10.3934/dcdsb.2020361

## Competitive exclusion in phytoplankton communities in a eutrophic water column

 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

Received  August 2020 Revised  October 2020 Published  April 2021 Early access  December 2020

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

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.

Citation: Robert Stephen Cantrell, King-Yeung Lam. Competitive exclusion in phytoplankton communities in a eutrophic water column. Discrete & Continuous Dynamical Systems - B, 2021, 26 (4) : 1783-1795. doi: 10.3934/dcdsb.2020361
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