Microbial growth in periodic gradostats
type: Item
instance of: scholarly article
title: Microbial growth in periodic gradostats
zbMATH Open document ID: 0726.92025
published in: Rocky Mountain Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: A gradostat is a laboratory device with which one can study the growth of microorganisms in a nutrient gradient. As constructed by \textit{R. W. Lovitt} and \textit{J. W. T. Wimpenny} [Soc. Gen. Microbial Quart. 6 (1979)] a gradostat is a concatenation of several chemostats in which adjacent vessels are connected by tubes allowing pumps to exchange the material contents of each vessel. The aim of the paper is to study a mathematical model of the growth of a single species of microorganisms in the presence of one limiting substrate or two limiting complementary substrates in a very general gradostat where essentially arbitrary connections between vessels are allowed. In addition, we allow operating parameters such as flow rates and reservoir nutrient concentration to vary periodically in time, simulating seasonal or diurnal variations in natural environments. The mathematical model reduces to a system of periodic, nonautonomous quasimonotone ordinary differential equations for species concentration in each vessel. The extinction or persistence of the population in the gradostat is determined by whether a certain dominant Floquet multiplier of a known quasimonotone linear periodic system either does not or does exceed unity. If the multiplier exceeds one then all nontrivial solutions are shown to approach a unique periodic steady state oscillation.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 92C99
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 4200042
zbMATH Keywords: seasonal variations
zbMATH Keywords: Perron-Frobenius theory
zbMATH Keywords: monotone dynamics
zbMATH Keywords: cooperative systems
zbMATH Keywords: gradostat
zbMATH Keywords: growth of microorganisms
zbMATH Keywords: chemostats
zbMATH Keywords: limiting substrate
zbMATH Keywords: limiting complementary substrates
zbMATH Keywords: flow rates
zbMATH Keywords: reservoir nutrient concentration
zbMATH Keywords: diurnal variations
zbMATH Keywords: system of periodic, nonautonomous quasimonotone ordinary differential equations
zbMATH Keywords: extinction
zbMATH Keywords: persistence
zbMATH Keywords: Floquet multiplier
zbMATH Keywords: periodic steady state oscillation
author: Hal L. Smith
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181073069
OpenAlex ID: W2028747408
cites work: Q3943082
cites work: Q3871201
cites work: Competition for fluctuating nutrient
cites work: A competition model for a seasonally fluctuating nutrient
cites work: Competition in the gradostat
cites work: Competitive Coexistence in an Oscillating Chemostat
cites work: Periodic Solutions of Periodic Competitive and Cooperative Systems
cites work: Cooperative systems of differential equations with concave nonlinearities
cites work: Competition in the gradostat: The role of the communication rate
cites work: Mathematical investigations of growth of microorganisms in the gradostat
cites work: A Mathematical Model of the Chemostat with Periodic Washout Rate
DOI: 10.1216/RMJM/1181073069
description: scientific article; zbMATH DE number 4200042