Competition in the gradostat: The role of the communication rate

DOI10.1007/BF00276100zbMath0716.92025OpenAlexW1980384879WikidataQ113909159 ScholiaQ113909159MaRDI QIDQ753727

Betty K. P. Tang, Hal Leslie Smith

Publication date: 1989

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00276100

zbMATH Keywords

competitioncoexistenceMichaelis-Menten kineticscooperative systemmonotone dynamical systemgradostatchemostatscommunication ratenutrient gradientoperating diagramssingle limiting nutrientspecies of microorganisms

Mathematics Subject Classification ID

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Ecology (92D40) Qualitative theory for ordinary differential equations (34C99) Asymptotic properties of solutions to ordinary differential equations (34D05) Physiological, cellular and medical topics (92C99)

Related Items (15)

A competition model in the chemostat with allelopathy and substrate inhibition ⋮ Competition models in the gradostat with general nutrient uptake functions ⋮ Asymptotically autonomous differential equations in the plane ⋮ Microbial predation in coupled chemostats: A global study of two coupled nonlinear oscillators ⋮ Steady-state coexistence of three pure and simple competitors in a four- membered reactor network ⋮ Source-sink dynamics and the coexistence of species on a single resource ⋮ Substrate inhibition can produce coexistence and limit cycles in the chemostat model with allelopathy ⋮ The operating diagram for a model of competition in a chemostat with an external lethal inhibitor ⋮ The growth of pure and simple microbial competitors in a moving distributed medium ⋮ Coexistence of three microbial populations competing for three complementary nutrients in a chemostat ⋮ Oscillations of two competing microbial populations in configurations of two interconnected chemostats ⋮ On the coexistence of three microbial populations competing for two complementary substrates in configurations of interconnected chemostats ⋮ Microbial growth in periodic gradostats ⋮ Global dynamics of the buffered chemostat for a general class of response functions ⋮ Equilibrium distribution of species among vessels of a gradostat. A singular perturbation approach

Cites Work

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• Mathematical investigations of growth of microorganisms in the gradostat
• Competition in the gradostat
• Competing Subcommunities of Mutualists and a Generalized Kamke Theorem
• Systems of Ordinary Differential Equations Which Generate an Order Preserving Flow. A Survey of Results
• A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms

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