Periodic Oscillations in a Chemostat Model with Two Discrete Delays
Periodic oscillations of solutions of a chemostat-type model in which a species feeds on a limiting nutrient are considered. The model incorporates two discrete delays representing the lag in nutrient recycling and nutrient conversion. Through the study of characteristic equation associated with the...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/306302 |
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| _version_ | 1849403776781254656 |
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| author | Tiansi Zhang Xuehui Ji Bo Li |
| author_facet | Tiansi Zhang Xuehui Ji Bo Li |
| author_sort | Tiansi Zhang |
| collection | DOAJ |
| description | Periodic oscillations of solutions of a chemostat-type model in which a species feeds on a limiting nutrient are considered. The model incorporates two discrete delays representing the lag in nutrient recycling and nutrient conversion. Through the study of characteristic equation associated with the linearized system, a unique positive equilibrium is found and proved to be locally asymptotically stable under some conditions. Meanwhile, a Hopf bifurcation causing periodic solutions is also obtained. Numerical simulations illustrate the theoretical results. |
| format | Article |
| id | doaj-art-83adcd0a2a304c238eda85f1ecb1d655 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-83adcd0a2a304c238eda85f1ecb1d6552025-08-20T03:37:11ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/306302306302Periodic Oscillations in a Chemostat Model with Two Discrete DelaysTiansi Zhang0Xuehui Ji1Bo Li2College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaPeriodic oscillations of solutions of a chemostat-type model in which a species feeds on a limiting nutrient are considered. The model incorporates two discrete delays representing the lag in nutrient recycling and nutrient conversion. Through the study of characteristic equation associated with the linearized system, a unique positive equilibrium is found and proved to be locally asymptotically stable under some conditions. Meanwhile, a Hopf bifurcation causing periodic solutions is also obtained. Numerical simulations illustrate the theoretical results.http://dx.doi.org/10.1155/2015/306302 |
| spellingShingle | Tiansi Zhang Xuehui Ji Bo Li Periodic Oscillations in a Chemostat Model with Two Discrete Delays Discrete Dynamics in Nature and Society |
| title | Periodic Oscillations in a Chemostat Model with Two Discrete Delays |
| title_full | Periodic Oscillations in a Chemostat Model with Two Discrete Delays |
| title_fullStr | Periodic Oscillations in a Chemostat Model with Two Discrete Delays |
| title_full_unstemmed | Periodic Oscillations in a Chemostat Model with Two Discrete Delays |
| title_short | Periodic Oscillations in a Chemostat Model with Two Discrete Delays |
| title_sort | periodic oscillations in a chemostat model with two discrete delays |
| url | http://dx.doi.org/10.1155/2015/306302 |
| work_keys_str_mv | AT tiansizhang periodicoscillationsinachemostatmodelwithtwodiscretedelays AT xuehuiji periodicoscillationsinachemostatmodelwithtwodiscretedelays AT boli periodicoscillationsinachemostatmodelwithtwodiscretedelays |