A Mathematical Model of the Chemostat with Periodic Washout Rate

• Published in: SIAM journal on applied mathematics Vol. 45; no. 3; pp. 435 - 449
• Main Authors: Butler, G. J., Hsu, S. B., Waltman, Paul
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.06.1985
• Subjects: Applied mathematics; Catalysis; Catalysts: preparations and properties; Catalytic reactions; Chemistry; Competition; Competitive exclusion; Differential equations; Ecological competition; Eigenvalues; Exact sciences and technology; Extinction; General and physical chemistry; General. Nomenclature, chemical documentation, computer chemistry; Laboratories; Linear transformations; Mathematical constants; Mathematical manifolds; Mathematical models; Theory of reactions, general kinetics; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry; Zero; Chemical reaction; Theory; Models
• ISSN: 0036-1399; 1095-712X
• DOI: 10.1137/0145025

In its simplest form, the chemostat consists of several populations of microorganisms competing for a single limiting nutrient. If the input concentration of nutrient and the washout rate are constant, theory predicts and experiment confirms that at most one of the populations will survive. In nature, however, one may expect the input concentration and washout rate to vary with time. In this paper we consider a model for the chemostat with periodic washout rate. Conditions are found for competitive exclusion to hold, and bifurcation techniques are employed to show that under suitable circumstances there will be coexistence of the competing populations in the form of positive periodic solutions.