Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy
The dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the lo...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/969425 |
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| _version_ | 1841524627215482880 |
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| author | Min Zhao Yanzhen Wang Lansun Chen |
| author_facet | Min Zhao Yanzhen Wang Lansun Chen |
| author_sort | Min Zhao |
| collection | DOAJ |
| description | The dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems. |
| format | Article |
| id | doaj-art-63735096878e47038ad1e050053e571a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-63735096878e47038ad1e050053e571a2025-02-03T05:47:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/969425969425Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control StrategyMin Zhao0Yanzhen Wang1Lansun Chen2School of Life and Environmental Science, Wenzhou University, Zhejiang, Wenzhou 325035, ChinaSchool of Mathematics and Information Science, Wenzhou University, Zhejiang, Wenzhou 325035, ChinaInstitute of Mathematics, Academia Sinica, Beijing 100080, ChinaThe dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.http://dx.doi.org/10.1155/2012/969425 |
| spellingShingle | Min Zhao Yanzhen Wang Lansun Chen Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy Journal of Applied Mathematics |
| title | Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy |
| title_full | Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy |
| title_fullStr | Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy |
| title_full_unstemmed | Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy |
| title_short | Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy |
| title_sort | dynamic analysis of a predator prey pest model with disease in prey and involving an impulsive control strategy |
| url | http://dx.doi.org/10.1155/2012/969425 |
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