Maintenance does not affect the stability of a two-tiered microbial 'food chain'
Résumé
Microbial 'food chains' are present in anaerobic digestion where the different reaction steps can be seen as such: the waste products of the organisms on one trophic level are consumed by organisms of the next trophic level. In the present paper we study a model of a two-tiered microbial food chain with feedback inhibition, which was recently presented as a stripped version of the anaerobic digestion model ADM1 of the International Water Association (IWA). It is known that in the absence of maintenance (or decay) the microbial 'food chain' is stable while its introduction in a number of models used in ecology may change their qualitative properties. In a recent paper Xu et al (2012), using a purely numerical approach and ADM1 consensus parameter values, it was shown that the model remains stable when decay terms are added. However, authors could not prove in full generality it remains true for other parameter values. In this paper we prove that introducing decay in the model preserves stability whatever its parameters values are and for a wide range of kinetics.
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