Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy
A generalized predator-prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of t...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/919242 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832554103472914432 |
|---|---|
| author | Wenjie Qin Guangyao Tang Sanyi Tang |
| author_facet | Wenjie Qin Guangyao Tang Sanyi Tang |
| author_sort | Wenjie Qin |
| collection | DOAJ |
| description | A generalized predator-prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given firstly. Once the threshold value exceeds a critical level, both pest and its natural enemy populations can oscillate periodically. Secondly, in order to address how the limited resources affect the pest control, as an example the Holling II functional response function is chosen. The numerical results show that predator-prey model with limited resource has complex dynamical behavior. In addition, it is confirmed that the model has the coexistence of pests and natural enemies for a wide range of parameters. |
| format | Article |
| id | doaj-art-9e7c6266b01a4cf7b8e64944ff3bd43a |
| 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-9e7c6266b01a4cf7b8e64944ff3bd43a2025-02-03T05:52:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/919242919242Generalized Predator-Prey Model with Nonlinear Impulsive Control StrategyWenjie Qin0Guangyao Tang1Sanyi Tang2College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaCollege of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaCollege of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaA generalized predator-prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given firstly. Once the threshold value exceeds a critical level, both pest and its natural enemy populations can oscillate periodically. Secondly, in order to address how the limited resources affect the pest control, as an example the Holling II functional response function is chosen. The numerical results show that predator-prey model with limited resource has complex dynamical behavior. In addition, it is confirmed that the model has the coexistence of pests and natural enemies for a wide range of parameters.http://dx.doi.org/10.1155/2014/919242 |
| spellingShingle | Wenjie Qin Guangyao Tang Sanyi Tang Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy Journal of Applied Mathematics |
| title | Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy |
| title_full | Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy |
| title_fullStr | Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy |
| title_full_unstemmed | Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy |
| title_short | Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy |
| title_sort | generalized predator prey model with nonlinear impulsive control strategy |
| url | http://dx.doi.org/10.1155/2014/919242 |
| work_keys_str_mv | AT wenjieqin generalizedpredatorpreymodelwithnonlinearimpulsivecontrolstrategy AT guangyaotang generalizedpredatorpreymodelwithnonlinearimpulsivecontrolstrategy AT sanyitang generalizedpredatorpreymodelwithnonlinearimpulsivecontrolstrategy |