Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays
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Journal of Advances in Mathematics and Computer Science
2024
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| Online Access: | https://repository.daystar.ac.ke/handle/123456789/4489 |
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| author | Ireri Jane , Pokhariyal Ganesh and Moindi Stephene |
| author_facet | Ireri Jane , Pokhariyal Ganesh and Moindi Stephene |
| author_sort | Ireri Jane , Pokhariyal Ganesh and Moindi Stephene |
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| description | Journal Article |
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| id | oai:repository.daystar.ac.ke:123456789-4489 |
| institution | Daystar University |
| language | English |
| publishDate | 2024 |
| publisher | Journal of Advances in Mathematics and Computer Science |
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| spelling | oai:repository.daystar.ac.ke:123456789-44892024-05-06T13:20:41Z Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays Ireri Jane , Pokhariyal Ganesh and Moindi Stephene Coexistence competition competitive exclusion DDE Periodic Chemostat Fourier series Hopf Bifurcation stability. Journal Article In 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. 2024-05-06T13:16:53Z 2024-05-06T13:16:53Z 2020 Article Ireri 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 2456-9968 https://repository.daystar.ac.ke/handle/123456789/4489 en 35(3) application/pdf Journal of Advances in Mathematics and Computer Science |
| spellingShingle | Coexistence competition competitive exclusion DDE Periodic Chemostat Fourier series Hopf Bifurcation stability. Ireri Jane , Pokhariyal Ganesh and Moindi Stephene Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays |
| title | Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays |
| title_full | Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays |
| title_fullStr | Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays |
| title_full_unstemmed | Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays |
| title_short | Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays |
| title_sort | hopf bifurcation analysis for a two species periodic chemostat model with discrete delays |
| topic | Coexistence competition competitive exclusion DDE Periodic Chemostat Fourier series Hopf Bifurcation stability. |
| url | https://repository.daystar.ac.ke/handle/123456789/4489 |
| work_keys_str_mv | AT irerijanepokhariyalganeshandmoindistephene hopfbifurcationanalysisforatwospeciesperiodicchemostatmodelwithdiscretedelays |
Hopf algebras 
Mutual inhibition, competition, and periodicity in a two species chemostat-like system /