Optimal Application Timing of Pest Control Tactics in Nonautonomous Pest Growth Model
Considering the effects of the living environment on growth of populations, it is unrealistic to assume that the growth rates of predator and prey are all constants in the models with integrated pest management (IPM) strategies. Therefore, a nonautonomous predator-prey system with impulsive effect i...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/650182 |
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| author | Shujuan Zhang Juhua Liang Sanyi Tang |
| author_facet | Shujuan Zhang Juhua Liang Sanyi Tang |
| author_sort | Shujuan Zhang |
| collection | DOAJ |
| description | Considering the effects of the living environment on growth of populations, it is unrealistic to assume that the growth rates of predator and prey are all constants in the models with integrated pest management (IPM) strategies. Therefore, a nonautonomous predator-prey system with impulsive effect is developed and investigated in the present work. In order to determine the optimal application timing of IPM tactics, the threshold value which guarantees the stability of pest-free periodic solution has been obtained firstly. The analytical formula of optimal application timings within a given period for different cases has been obtained such that the threshold value is the smallest, which is the most effective in successful pest control. Moreover, extensively numerical investigations have also been confirmed our main results and the biological implications have been discussed in more detail. The main results can guide the farmer to design the optimal pest control strategies. |
| format | Article |
| id | doaj-art-48d5576b916d48e9b7e930434ed560ba |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-48d5576b916d48e9b7e930434ed560ba2025-02-03T01:06:41ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/650182650182Optimal Application Timing of Pest Control Tactics in Nonautonomous Pest Growth ModelShujuan Zhang0Juhua Liang1Sanyi 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, ChinaConsidering the effects of the living environment on growth of populations, it is unrealistic to assume that the growth rates of predator and prey are all constants in the models with integrated pest management (IPM) strategies. Therefore, a nonautonomous predator-prey system with impulsive effect is developed and investigated in the present work. In order to determine the optimal application timing of IPM tactics, the threshold value which guarantees the stability of pest-free periodic solution has been obtained firstly. The analytical formula of optimal application timings within a given period for different cases has been obtained such that the threshold value is the smallest, which is the most effective in successful pest control. Moreover, extensively numerical investigations have also been confirmed our main results and the biological implications have been discussed in more detail. The main results can guide the farmer to design the optimal pest control strategies.http://dx.doi.org/10.1155/2014/650182 |
| spellingShingle | Shujuan Zhang Juhua Liang Sanyi Tang Optimal Application Timing of Pest Control Tactics in Nonautonomous Pest Growth Model Abstract and Applied Analysis |
| title | Optimal Application Timing of Pest Control Tactics in Nonautonomous Pest Growth Model |
| title_full | Optimal Application Timing of Pest Control Tactics in Nonautonomous Pest Growth Model |
| title_fullStr | Optimal Application Timing of Pest Control Tactics in Nonautonomous Pest Growth Model |
| title_full_unstemmed | Optimal Application Timing of Pest Control Tactics in Nonautonomous Pest Growth Model |
| title_short | Optimal Application Timing of Pest Control Tactics in Nonautonomous Pest Growth Model |
| title_sort | optimal application timing of pest control tactics in nonautonomous pest growth model |
| url | http://dx.doi.org/10.1155/2014/650182 |
| work_keys_str_mv | AT shujuanzhang optimalapplicationtimingofpestcontroltacticsinnonautonomouspestgrowthmodel AT juhualiang optimalapplicationtimingofpestcontroltacticsinnonautonomouspestgrowthmodel AT sanyitang optimalapplicationtimingofpestcontroltacticsinnonautonomouspestgrowthmodel |