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Breakdown of a Chemostat Exposed to Stochastic Noise

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The stochastic dynamics of a chemostat with three trophic levels, substrate-bacterium-worm, is analyzed. It is assumed that the worm population is perturbed by environmental stochastic noise causing extinction in finite time. A diffusion model of the process is formulated. With singular perturbation methods applied to the corresponding Fokker-Planck equation an estimate of the expected extinction time is derived. This chemostat can be seen as an experimental sewage-treatment system in which the worm population facilitates the reduction of remaining sludge

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Correspondence to Johan Grasman.

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Grasman, J., Gee, M.D. & Herwaarden, O.A.V. Breakdown of a Chemostat Exposed to Stochastic Noise. J Eng Math 53, 291–300 (2005).

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