Mathematical investigations of growth of microorganisms in the gradostat
type: Item
instance of: scholarly article
title: Mathematical investigations of growth of microorganisms in the gradostat
zbMATH Open document ID: 0604.92020
DOI: 10.1007/BF00275252
published in: Journal of Mathematical Biology
publication date: 1986-01-01T00:00:00Z
review text: The author investigates analytically and numerically the growth of a single species of microorganisms in the gradostat, finding that the growth can be described by a mathematical model similar to that one for the chemostat, assuming Michaelis-Menten kinetics of uptake of substrate by the microorganisms. The model for the cases where there is a gradient of one limiting substrate, and where there are opposing gradients of two limiting complementary substrates is a system of 2n and, respectively, 3n equations - n being the number of vessels. The solutions of the system of nonlinear algebraic equations are considered as fixed points of an operator in an ordered Banach space, and the global bifurcation from the trivial solution is studied. The nontrivial solution is obtained numerically and qualitatively analyzed. The expectation that concentrations of the microorganisms are maximum close to the source and decreasing gradually along the series of vessels is confirmed if the parameters are not close to the bifurcation values. On the contrary, when there are two limiting complementary substrates in opposing gradients, microorganisms concentrate most in the middle of the gradostat, only if the parameters are close to the bifurcation values. The analysis shows that growth of microorganisms in the gradostat does not depend on their initial concentration, the transport between the vessels having a significant effect on the growth rate. Thus, different transport rates give different asymptotic behaviours.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 3976850
zbMATH Keywords: microbial ecosystems
zbMATH Keywords: series of coupled chemostats
zbMATH Keywords: sublinear operator
zbMATH Keywords: spatial distribution
zbMATH Keywords: gradostat
zbMATH Keywords: Michaelis-Menten kinetics
zbMATH Keywords: limiting complementary substrates
zbMATH Keywords: nonlinear algebraic equations
zbMATH Keywords: fixed points
zbMATH Keywords: ordered Banach space
zbMATH Keywords: bifurcation values
zbMATH Keywords: growth of microorganisms
zbMATH Keywords: transport rates
Wikidata QID: Q113909322
author: Betty K. P. Tang
reviewed by: Cristina Irimia
MaRDI profile type: Publication
cites work: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
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full work available at URL: https://doi.org/10.1007/bf00275252
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description: scientific article; zbMATH DE number 3976850