Smith, F; Velayudhan, A; Voulgarelis, D; (2018) Stochastic analysis of a full system of two competing populations in a chemostat. Chemical Engineering Science , 175 pp. 424-444. 10.1016/j.ces.2017.10.052.

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Abstract

This paper formulates two 3D models using stochastic differential equations (SDEs) of two microbial populations in a chemostat competing over a single substrate. These models have two distinct noise sources. One is general noise whereas the other is dilution-rate-induced noise. Nonlinear Monod growth rates are assumed and the paper is mainly focused on the parameter values where coexistence is found in the deterministic model. Nondimensionalising the equations around the point of intersection of the two growth rates identifies the dimensionless substrate feed as a large parameter. This in turn is used to perform an asymptotic analysis leading to a reduced 2D system of equations describing the dynamics of the populations on and close to a line of steady states obtained previously from the deterministic stability analysis. That reduced system allows the formulation of a spatially 2D Fokker-Planck equation which, when solved numerically, admits results similar to those from the SDEs. Contrary to previous suggestions, one particular population becomes dominant at large times. Finally, we briefly explore the case where death rates are included.

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