Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control
The application of pest management involves two thresholds when the chemical control and biological control are adopted, respectively. Our purpose is to provide an appropriate balance between the chemical control and biological control. Therefore, a Smith predator-prey system for integrated pest man...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/4945728 |
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| author | Yaning Li Yan Li Yu Liu Huidong Cheng |
| author_facet | Yaning Li Yan Li Yu Liu Huidong Cheng |
| author_sort | Yaning Li |
| collection | DOAJ |
| description | The application of pest management involves two thresholds when the chemical control and biological control are adopted, respectively. Our purpose is to provide an appropriate balance between the chemical control and biological control. Therefore, a Smith predator-prey system for integrated pest management is established in this paper. In this model, the intensity of implementation of biological control and chemical control depends linearly on the selected control level (threshold). Firstly, the existence and uniqueness of the order-one periodic solution (i.e., OOPS) are proved by means of the subsequent function method to confirm the feasibility of the biological and chemical control strategy of pest management. Secondly, the stability of system is proved by the limit method of the successor points’ sequences and the analogue of the Poincaré criterion. Moreover, an optimization strategy is formulated to reduce the total cost and obtain the best level of pest control. Finally, the numerical simulation of a specific model is performed. |
| format | Article |
| id | doaj-art-7c23d0b42fd748408eff1d47a2000cb9 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-7c23d0b42fd748408eff1d47a2000cb92025-08-20T02:06:53ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/49457284945728Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback ControlYaning Li0Yan Li1Yu Liu2Huidong Cheng3College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Foreign Languages, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaThe application of pest management involves two thresholds when the chemical control and biological control are adopted, respectively. Our purpose is to provide an appropriate balance between the chemical control and biological control. Therefore, a Smith predator-prey system for integrated pest management is established in this paper. In this model, the intensity of implementation of biological control and chemical control depends linearly on the selected control level (threshold). Firstly, the existence and uniqueness of the order-one periodic solution (i.e., OOPS) are proved by means of the subsequent function method to confirm the feasibility of the biological and chemical control strategy of pest management. Secondly, the stability of system is proved by the limit method of the successor points’ sequences and the analogue of the Poincaré criterion. Moreover, an optimization strategy is formulated to reduce the total cost and obtain the best level of pest control. Finally, the numerical simulation of a specific model is performed.http://dx.doi.org/10.1155/2018/4945728 |
| spellingShingle | Yaning Li Yan Li Yu Liu Huidong Cheng Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control Discrete Dynamics in Nature and Society |
| title | Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control |
| title_full | Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control |
| title_fullStr | Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control |
| title_full_unstemmed | Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control |
| title_short | Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control |
| title_sort | stability analysis and control optimization of a prey predator model with linear feedback control |
| url | http://dx.doi.org/10.1155/2018/4945728 |
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