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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