A Predator-Prey Model in the Chemostat with Time Delay
The aim of this paper is to study the dynamics of predator-prey interaction in a chemostat to determine whether including a discrete delay to model the time between the capture of the prey and its conversion to viable biomass can introduce oscillatory dynamics even though there is a globally asympto...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/287969 |
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| _version_ | 1832549113858621440 |
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| author | Guihong Fan Gail S. K. Wolkowicz |
| author_facet | Guihong Fan Gail S. K. Wolkowicz |
| author_sort | Guihong Fan |
| collection | DOAJ |
| description | The aim of this paper is to study the dynamics of predator-prey interaction in a chemostat to determine whether including a discrete delay to model the time between the capture of the prey and its conversion to viable biomass can introduce oscillatory dynamics even though there is a globally asymptotically stable equilibrium when the delay is ignored. Hence, Holling type I response functions are chosen so that no oscillatory behavior is possible when there is no delay. It is proven that unlike the analogous model for competition, as the parameter modeling the delay is increased, Hopf bifurcations can occur. |
| format | Article |
| id | doaj-art-90f2ecdceaeb4b70a0cb1ae6647d33e8 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-90f2ecdceaeb4b70a0cb1ae6647d33e82025-02-03T06:12:09ZengWileyInternational Journal of Differential Equations1687-96431687-96512010-01-01201010.1155/2010/287969287969A Predator-Prey Model in the Chemostat with Time DelayGuihong Fan0Gail S. K. Wolkowicz1Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, CanadaDepartment of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, CanadaThe aim of this paper is to study the dynamics of predator-prey interaction in a chemostat to determine whether including a discrete delay to model the time between the capture of the prey and its conversion to viable biomass can introduce oscillatory dynamics even though there is a globally asymptotically stable equilibrium when the delay is ignored. Hence, Holling type I response functions are chosen so that no oscillatory behavior is possible when there is no delay. It is proven that unlike the analogous model for competition, as the parameter modeling the delay is increased, Hopf bifurcations can occur.http://dx.doi.org/10.1155/2010/287969 |
| spellingShingle | Guihong Fan Gail S. K. Wolkowicz A Predator-Prey Model in the Chemostat with Time Delay International Journal of Differential Equations |
| title | A Predator-Prey Model in the Chemostat with Time Delay |
| title_full | A Predator-Prey Model in the Chemostat with Time Delay |
| title_fullStr | A Predator-Prey Model in the Chemostat with Time Delay |
| title_full_unstemmed | A Predator-Prey Model in the Chemostat with Time Delay |
| title_short | A Predator-Prey Model in the Chemostat with Time Delay |
| title_sort | predator prey model in the chemostat with time delay |
| url | http://dx.doi.org/10.1155/2010/287969 |
| work_keys_str_mv | AT guihongfan apredatorpreymodelinthechemostatwithtimedelay AT gailskwolkowicz apredatorpreymodelinthechemostatwithtimedelay AT guihongfan predatorpreymodelinthechemostatwithtimedelay AT gailskwolkowicz predatorpreymodelinthechemostatwithtimedelay |