Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the Prey
The Allee effect is incorporated into a predator-prey model with linear functional response. Compared with the predator-prey which only takes the crowding effect and predator partially dependent on prey into consideration, it is found that the Allee effect of the prey species would increase the exti...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/4275372 |
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| author | Jie Yan Chunli Li Xueli Chen Lishun Ren |
| author_facet | Jie Yan Chunli Li Xueli Chen Lishun Ren |
| author_sort | Jie Yan |
| collection | DOAJ |
| description | The Allee effect is incorporated into a predator-prey model with linear functional response. Compared with the predator-prey which only takes the crowding effect and predator partially dependent on prey into consideration, it is found that the Allee effect of the prey species would increase the extinction risk of both the prey and predator. Moreover, by using a center manifold theorem and bifurcation theory, it is shown that the model with Allee effect undergoes the flip bifurcation and Hopf bifurcation in the interior of R+2 with different Allee effect values. In the two bifurcations, we can come to the conclusion that different Allee effect will have different bifurcation value and the increasing of the Allee effect will increase the value of bifurcation, respectively. |
| format | Article |
| id | doaj-art-cdf0e89e2dca4f938535422cf7d3fd08 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-cdf0e89e2dca4f938535422cf7d3fd082025-08-20T03:19:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/42753724275372Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the PreyJie Yan0Chunli Li1Xueli Chen2Lishun Ren3Department of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466000, ChinaDepartment of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466000, ChinaDepartment of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466000, ChinaDepartment of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466000, ChinaThe Allee effect is incorporated into a predator-prey model with linear functional response. Compared with the predator-prey which only takes the crowding effect and predator partially dependent on prey into consideration, it is found that the Allee effect of the prey species would increase the extinction risk of both the prey and predator. Moreover, by using a center manifold theorem and bifurcation theory, it is shown that the model with Allee effect undergoes the flip bifurcation and Hopf bifurcation in the interior of R+2 with different Allee effect values. In the two bifurcations, we can come to the conclusion that different Allee effect will have different bifurcation value and the increasing of the Allee effect will increase the value of bifurcation, respectively.http://dx.doi.org/10.1155/2016/4275372 |
| spellingShingle | Jie Yan Chunli Li Xueli Chen Lishun Ren Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the Prey Discrete Dynamics in Nature and Society |
| title | Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the Prey |
| title_full | Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the Prey |
| title_fullStr | Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the Prey |
| title_full_unstemmed | Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the Prey |
| title_short | Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the Prey |
| title_sort | dynamic complexities in 2 dimensional discrete time predator prey systems with allee effect in the prey |
| url | http://dx.doi.org/10.1155/2016/4275372 |
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