A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey
We introduce and study a Gompertz model with time delay and impulsive perturbations on the prey. By using the discrete dynamical system determined by the stroboscopic map, we obtain the sufficient conditions for the existence and global attractivity of the “predator-extinction” periodic solution. Wi...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/256195 |
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| _version_ | 1832555994516815872 |
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| author | Jianwen Jia Chunhua Li |
| author_facet | Jianwen Jia Chunhua Li |
| author_sort | Jianwen Jia |
| collection | DOAJ |
| description | We introduce and study a Gompertz model with time delay and impulsive perturbations on the prey. By using the discrete dynamical system determined by the stroboscopic map, we obtain the sufficient conditions for the existence and global attractivity of the “predator-extinction” periodic solution. With the theory on the delay functional and impulsive differential equation, we obtain the appropriate condition for the permanence of the system. |
| format | Article |
| id | doaj-art-70ebf33b75164615aa663d63977bdcc8 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-70ebf33b75164615aa663d63977bdcc82025-02-03T05:46:43ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/256195256195A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the PreyJianwen Jia0Chunhua Li1School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, ChinaSchool of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, ChinaWe introduce and study a Gompertz model with time delay and impulsive perturbations on the prey. By using the discrete dynamical system determined by the stroboscopic map, we obtain the sufficient conditions for the existence and global attractivity of the “predator-extinction” periodic solution. With the theory on the delay functional and impulsive differential equation, we obtain the appropriate condition for the permanence of the system.http://dx.doi.org/10.1155/2009/256195 |
| spellingShingle | Jianwen Jia Chunhua Li A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey Discrete Dynamics in Nature and Society |
| title | A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey |
| title_full | A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey |
| title_fullStr | A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey |
| title_full_unstemmed | A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey |
| title_short | A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey |
| title_sort | predator prey gompertz model with time delay and impulsive perturbations on the prey |
| url | http://dx.doi.org/10.1155/2009/256195 |
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