Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model
An integrated pest management prey-predator model with ratio-dependent and impulsive feedback control is investigated in this paper. Firstly, we determine the Poincaré map which is defined on the phase set and discuss its main properties including monotonicity, continuity, and discontinuity. Secondl...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2376374 |
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| _version_ | 1849691103651954688 |
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| author | Zhenzhen Shi Qingjian Li Weiming Li Huidong Cheng |
| author_facet | Zhenzhen Shi Qingjian Li Weiming Li Huidong Cheng |
| author_sort | Zhenzhen Shi |
| collection | DOAJ |
| description | An integrated pest management prey-predator model with ratio-dependent and impulsive feedback control is investigated in this paper. Firstly, we determine the Poincaré map which is defined on the phase set and discuss its main properties including monotonicity, continuity, and discontinuity. Secondly, the existence and stability of the boundary order-one periodic solution are proved by the method of Poincaré map. According to the Poincaré map and related differential equation theory, the conditions of the existence and global stability of the order-one periodic solution are obtained when ΦyA<yA, and we prove the sufficient and necessary conditions for the global asymptotic stability of the order-one periodic solution when ΦyA>yA. Furthermore, we prove the existence of the order-kk≥2 periodic solution under certain conditions. Finally, we verify the main results by numerical simulation. |
| format | Article |
| id | doaj-art-e274916c163c4c29bf50ddfe6dfe5fed |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-e274916c163c4c29bf50ddfe6dfe5fed2025-08-20T03:21:08ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/23763742376374Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator ModelZhenzhen Shi0Qingjian Li1Weiming Li2Huidong Cheng3College of Mathematics and System Sciences, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaCollege of Foreign Languages, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaCollege of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaCollege of Mathematics and System Sciences, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaAn integrated pest management prey-predator model with ratio-dependent and impulsive feedback control is investigated in this paper. Firstly, we determine the Poincaré map which is defined on the phase set and discuss its main properties including monotonicity, continuity, and discontinuity. Secondly, the existence and stability of the boundary order-one periodic solution are proved by the method of Poincaré map. According to the Poincaré map and related differential equation theory, the conditions of the existence and global stability of the order-one periodic solution are obtained when ΦyA<yA, and we prove the sufficient and necessary conditions for the global asymptotic stability of the order-one periodic solution when ΦyA>yA. Furthermore, we prove the existence of the order-kk≥2 periodic solution under certain conditions. Finally, we verify the main results by numerical simulation.http://dx.doi.org/10.1155/2020/2376374 |
| spellingShingle | Zhenzhen Shi Qingjian Li Weiming Li Huidong Cheng Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model Complexity |
| title | Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model |
| title_full | Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model |
| title_fullStr | Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model |
| title_full_unstemmed | Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model |
| title_short | Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model |
| title_sort | poincare map approach to global dynamics of the integrated pest management prey predator model |
| url | http://dx.doi.org/10.1155/2020/2376374 |
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