Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses
A class of Holling type II predator-prey systems with mutual interference and impulses is presented. Sufficient conditions for the permanence, extinction, and global attractivity of system are obtained. The existence and uniqueness of positive periodic solution are also established. Numerical simula...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/793761 |
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| _version_ | 1832545282424832000 |
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| author | Hongli Li Long Zhang Zhidong Teng Yaolin Jiang |
| author_facet | Hongli Li Long Zhang Zhidong Teng Yaolin Jiang |
| author_sort | Hongli Li |
| collection | DOAJ |
| description | A class of Holling type II predator-prey systems with mutual interference and impulses is presented. Sufficient conditions for the permanence, extinction, and global attractivity of system are obtained. The existence and uniqueness of positive periodic solution are also established. Numerical simulations are carried out to illustrate the theoretical results. Meanwhile, they indicate that dynamics of species are very sensitive with the period matching between species’ intrinsic disciplinarians and the perturbations from the variable environment. If the periods between individual growth and impulse perturbations match well, then the dynamics of species periodically change. If they mismatch each other, the dynamics differ from period to period until there is chaos. |
| format | Article |
| id | doaj-art-17477391a7384f6fbf7b2788d009674e |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-17477391a7384f6fbf7b2788d009674e2025-02-03T07:26:17ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/793761793761Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and ImpulsesHongli Li0Long Zhang1Zhidong Teng2Yaolin Jiang3College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaA class of Holling type II predator-prey systems with mutual interference and impulses is presented. Sufficient conditions for the permanence, extinction, and global attractivity of system are obtained. The existence and uniqueness of positive periodic solution are also established. Numerical simulations are carried out to illustrate the theoretical results. Meanwhile, they indicate that dynamics of species are very sensitive with the period matching between species’ intrinsic disciplinarians and the perturbations from the variable environment. If the periods between individual growth and impulse perturbations match well, then the dynamics of species periodically change. If they mismatch each other, the dynamics differ from period to period until there is chaos.http://dx.doi.org/10.1155/2014/793761 |
| spellingShingle | Hongli Li Long Zhang Zhidong Teng Yaolin Jiang Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses Discrete Dynamics in Nature and Society |
| title | Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses |
| title_full | Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses |
| title_fullStr | Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses |
| title_full_unstemmed | Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses |
| title_short | Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses |
| title_sort | dynamic behaviors of holling type ii predator prey system with mutual interference and impulses |
| url | http://dx.doi.org/10.1155/2014/793761 |
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