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A new proof of the competitive exclusion principle in the chemostat

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  • We give an new proof of the well-known competitive exclusion principle in the chemostat model with $N$ species competing for a single resource, for any set of increasing growth functions. The proof is constructed by induction on the number of the species, after being ordered. It uses elementary analysis and comparisons of solutions of ordinary differential equations.

    Mathematics Subject Classification: 34K20, 92D25.

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  • Figure 1.  Growth functions and their break-even concentrations

    Figure 2.  Illustration of the intervals $I_{i} = [s_1^-, s_i^+]$ for $i\in\{1, \cdots, N-1\}$ (in green, the values of the break-even concentrations $\lambda_{i}$, in orange, the nested intervals $I_{i}$)

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