Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input
The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/830951 |
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| _version_ | 1832562723454451712 |
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| author | Kai Wang Zhidong Teng Fengqin Zhang |
| author_facet | Kai Wang Zhidong Teng Fengqin Zhang |
| author_sort | Kai Wang |
| collection | DOAJ |
| description | The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established. Finally, an example is given to demonstrate the effectiveness of the results in this paper. |
| format | Article |
| id | doaj-art-2c9413f3ad1a4e1da781f8df93262213 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2c9413f3ad1a4e1da781f8df932622132025-02-03T01:21:51ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/830951830951Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed InputKai Wang0Zhidong Teng1Fengqin Zhang2College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaDepartment of Mathematics, Yuncheng University, Yuncheng 044000, ChinaThe dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.http://dx.doi.org/10.1155/2010/830951 |
| spellingShingle | Kai Wang Zhidong Teng Fengqin Zhang Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input Discrete Dynamics in Nature and Society |
| title | Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input |
| title_full | Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input |
| title_fullStr | Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input |
| title_full_unstemmed | Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input |
| title_short | Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input |
| title_sort | global behaviors of a chemostat model with delayed nutrient recycling and periodically pulsed input |
| url | http://dx.doi.org/10.1155/2010/830951 |
| work_keys_str_mv | AT kaiwang globalbehaviorsofachemostatmodelwithdelayednutrientrecyclingandperiodicallypulsedinput AT zhidongteng globalbehaviorsofachemostatmodelwithdelayednutrientrecyclingandperiodicallypulsedinput AT fengqinzhang globalbehaviorsofachemostatmodelwithdelayednutrientrecyclingandperiodicallypulsedinput |