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The dynamics of a reaction-diffusion system for two species of microorganism
in an unstirred chemostat with internal storage is studied.
It is shown that the diffusion coefficient is a key parameter
of determining the asymptotic dynamics, and there exists a threshold
diffusion coefficient above which both species become extinct.
On the other hand, for diffusion coefficient below the threshold,
either one species or both species persist, and in the asymptotic
limit, a steady state showing competition exclusion or coexistence
is reached.
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