Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays

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dc.contributor.authorMoindi, Stephene
dc.contributor.authorIreri, Jane
dc.contributor.authorPokhariyal, Ganesh
dc.date.accessioned2024-05-06T13:16:53Z
dc.date.available2024-05-06T13:16:53Z
dc.date.issued2020
dc.descriptionJournal Article
dc.description.abstractIn this paper we analyze a Chemostat model of two species competing for a single limiting nutrient input varied periodically using a Fourier series with discrete delays. To understand global aspects of the dynamics we use an extension of the Hopf bifurcation theorem, a method that rigorously establishes existence of a periodic solution. We show that the interior equilibrium point changes its stability and due to the delay parameter it undergoes a Hopf bifurcation. Numerical results shows that coexistence is possible when delays are introduced and Fourier series produces the required seasonal variations. We also show that for small delays periodic variations of nutrients has more influence on species density variations than the delay.
dc.identifier.citationIreri J., Pokhariyal G., and Moindi S. (2020): Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays. Journal of Advances in Mathematics and Computer Science
dc.identifier.issn2456-9968
dc.identifier.urihttps://repository.daystar.ac.ke/handle/123456789/4489
dc.language.isoen
dc.publisherJournal of Advances in Mathematics and Computer Science
dc.relation.ispartofseries35(3)
dc.subjectCoexistence
dc.subjectcompetition
dc.subjectcompetitive exclusion
dc.subjectDDE
dc.subjectPeriodic Chemostat
dc.subjectFourier series
dc.subjectHopf Bifurcation
dc.subjectstability.
dc.titleHopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays
dc.typeArticle

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