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Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Department of Mathematics, Jiangsu University, Zhenjiang, 212013, Jiangsu Province, P. R. China.
2009 (English)In: Applied mathematics and mechanics, ISSN 0253-4827, E-ISSN 1573-2754, Vol. 30, no 7, 933-944 p.Article in journal (Refereed) PublishedText
Abstract [en]

In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nutrient refilling and the periodic antibiotic injection occur with the same periodicity, but not simultaneously. The model is then formulated in terms of autonomous differential equations subject to impulsive perturbations. It is observed that either the population of microorganisms essentially washes out, or more favorably, the system is permanent. To describe this dichotomy, some biologically significant integral conditions are introduced. Further, it is shown that in a certain critical situation, a nontrivial periodic solution emerges via a bifurcation phenomenon. Finally, the dynamics of the model is illustrated with numerical experiments and computer simulations.

Place, publisher, year, edition, pages
Springer Netherlands, 2009. Vol. 30, no 7, 933-944 p.
Keyword [en]
chemostat, impulsive differential equation, permanence, extinction, fixed point approach, bifurcation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-115987DOI: 10.1007/s10483-009-0712-xISI: 000268187900012OAI: oai:DiVA.org:umu-115987DiVA: diva2:907081
Available from: 2016-02-26 Created: 2016-02-08 Last updated: 2016-02-26Bibliographically approved

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Zhang, Hong
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ReferencesLink to record
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