Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting
Two predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the periodic solution and analyse the dynamic phen...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/803764 |
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| _version_ | 1849305086400921600 |
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| author | Mingzhan Huang Xinyu Song |
| author_facet | Mingzhan Huang Xinyu Song |
| author_sort | Mingzhan Huang |
| collection | DOAJ |
| description | Two predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the periodic solution and analyse the dynamic phenomenon of homoclinic bifurcation of the first system by choosing the harvesting rate β as control parameter. Besides, we also study the homoclinic bifurcation of the second system about parameter δ on the basis of the theory of rotated vector field. Finally, numerical simulations are presented to illustrate the results. |
| format | Article |
| id | doaj-art-0b7985dbfb3a4cc2977d3e8407f897a3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-0b7985dbfb3a4cc2977d3e8407f897a32025-08-20T03:55:32ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/803764803764Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive HarvestingMingzhan Huang0Xinyu Song1Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091, ChinaCollege of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, ChinaTwo predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the periodic solution and analyse the dynamic phenomenon of homoclinic bifurcation of the first system by choosing the harvesting rate β as control parameter. Besides, we also study the homoclinic bifurcation of the second system about parameter δ on the basis of the theory of rotated vector field. Finally, numerical simulations are presented to illustrate the results.http://dx.doi.org/10.1155/2014/803764 |
| spellingShingle | Mingzhan Huang Xinyu Song Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting Journal of Applied Mathematics |
| title | Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting |
| title_full | Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting |
| title_fullStr | Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting |
| title_full_unstemmed | Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting |
| title_short | Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting |
| title_sort | periodic solutions and homoclinic bifurcations of two predator prey systems with nonmonotonic functional response and impulsive harvesting |
| url | http://dx.doi.org/10.1155/2014/803764 |
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