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Zbl 1158.92328
Grasman, Johan; Gee, Maarten De; Herwaarden, Onno A.Van
Breakdown of a chemostat exposed to stochastic noise. (English)
[J] J. Eng. Math. 53, No. 3-4, 291-300 (2005). ISSN 0022-0833; ISSN 1573-2703/e

Summary: The stochastic dynamics of a chemostat with three trophic levels, substrate -- bacter\-ium -- 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

MSC 2000:: *92D40 Ecology
60J70 Appl. of diffusion theory

Keywords: chemostat; Fokker-Planck equation; white noise; WKB-method

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Zentralblatt MATH Berlin [Germany]