Stability and robustness analysis for a multispecies chemostat model with delays in the growth rates and uncertainties | Zendy

Frédéric Mazenc | Zendy; Gonzalo Robledo | Zendy; Michael Malisoff | Zendy

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Stability and robustness analysis for a multispecies chemostat model with delays in the growth rates and uncertainties

Author(s) -

Frédéric Mazenc,

Gonzalo Robledo,

Michael Malisoff

Publication year - 2018

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2018098

Subject(s) - chemostat , robustness (evolution) , control theory (sociology) , constant (computer programming) , stability (learning theory) , dilution , exponential stability , mathematics , computer science , physics , chemistry , thermodynamics , biology , biochemistry , genetics , control (management) , nonlinear system , quantum mechanics , artificial intelligence , machine learning , bacteria , gene , programming language

We study a chemostat model with an arbitrary number of competing species, one substrate, and constant dilution rates. We allow delays in the growth rates and additive uncertainties. Using constant inputs of certain species, we derive bounds on the sizes of the delays that ensure asymptotic stability of an equilibrium when the uncertainties are zero, which can allow persistence of multiple species. Under delays and uncertainties, we provide bounds on the delays and on the uncertainties that ensure input-to-state stability with respect to uncertainties.

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