Breakdown time 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
Original languageEnglish
Pages (from-to)291-300
Number of pages9
JournalJournal of Engineering Mathematics
Issue number3-4
Publication statusPublished - 2005


  • extinction
  • epidemics


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