Chaos in a Predator-Prey System with Impulsive Perturbations and Stage Structure for the Predator
We investigate a predator-prey model with stage structure for the predator and periodic constant impulsive perturbations. Conditions for extinction of prey and immature predator are given. By using the Floquet theory and small amplitude perturbation skills, we consider the local stability of prey, i...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/195382 |
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| _version_ | 1832566912647692288 |
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| author | Bin Zhang Shuai Shi Woye Liu |
| author_facet | Bin Zhang Shuai Shi Woye Liu |
| author_sort | Bin Zhang |
| collection | DOAJ |
| description | We investigate a predator-prey model with stage structure for the predator and periodic constant impulsive perturbations. Conditions for extinction of prey and immature predator are given. By using the Floquet theory and small amplitude perturbation skills, we consider the local stability of prey, immature predator eradication periodic solution. Furthermore, by using the method of numerical simulation, the influence of the impulsive control strategy on the inherent oscillation is investigated, which shows rich complex dynamic (such as periodic doubling bifurcation, periodic halving bifurcation, nonunique attractors, chaos, and periodic windows). |
| format | Article |
| id | doaj-art-a739ed88528e45d497025c84ed3c321e |
| 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-a739ed88528e45d497025c84ed3c321e2025-02-03T01:02:48ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/195382195382Chaos in a Predator-Prey System with Impulsive Perturbations and Stage Structure for the PredatorBin Zhang0Shuai Shi1Woye Liu2Fifth Department, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaFifth Department, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaFifth Department, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaWe investigate a predator-prey model with stage structure for the predator and periodic constant impulsive perturbations. Conditions for extinction of prey and immature predator are given. By using the Floquet theory and small amplitude perturbation skills, we consider the local stability of prey, immature predator eradication periodic solution. Furthermore, by using the method of numerical simulation, the influence of the impulsive control strategy on the inherent oscillation is investigated, which shows rich complex dynamic (such as periodic doubling bifurcation, periodic halving bifurcation, nonunique attractors, chaos, and periodic windows).http://dx.doi.org/10.1155/2009/195382 |
| spellingShingle | Bin Zhang Shuai Shi Woye Liu Chaos in a Predator-Prey System with Impulsive Perturbations and Stage Structure for the Predator Discrete Dynamics in Nature and Society |
| title | Chaos in a Predator-Prey System with Impulsive Perturbations and Stage Structure for the Predator |
| title_full | Chaos in a Predator-Prey System with Impulsive Perturbations and Stage Structure for the Predator |
| title_fullStr | Chaos in a Predator-Prey System with Impulsive Perturbations and Stage Structure for the Predator |
| title_full_unstemmed | Chaos in a Predator-Prey System with Impulsive Perturbations and Stage Structure for the Predator |
| title_short | Chaos in a Predator-Prey System with Impulsive Perturbations and Stage Structure for the Predator |
| title_sort | chaos in a predator prey system with impulsive perturbations and stage structure for the predator |
| url | http://dx.doi.org/10.1155/2009/195382 |
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