Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource Management
In this paper, mathematical models for the management of biological resources based on a given predator-prey relationship are proposed, and two types of control strategies, unilateral and bilateral control with impulsive state feedback, are studied. The existence of the order-1 homoclinic orbit, ord...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/9453941 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841524420648108032 |
|---|---|
| author | Mingzhan Huang Shouzong Liu Xinyu Song Lansun Chen |
| author_facet | Mingzhan Huang Shouzong Liu Xinyu Song Lansun Chen |
| author_sort | Mingzhan Huang |
| collection | DOAJ |
| description | In this paper, mathematical models for the management of biological resources based on a given predator-prey relationship are proposed, and two types of control strategies, unilateral and bilateral control with impulsive state feedback, are studied. The existence of the order-1 homoclinic orbit, order-1 periodic solution, and bifurcation of homoclinic of the unilateral control system are obtained, and the attraction region of this system is also discussed. Besides, sufficient conditions for the existence and stability of the order-1 and order-2 periodic solutions of the bilateral control system are also gained. A series of numerical simulations including bifurcation diagrams of periodic solution are performed, which not only verify the theoretical results we get but also reveal some peculiar dynamical phenomena, such as the appearance of high-order periodic solutions and existence of parameter intervals with drastic order change of periodic solution. By comparing the two management strategies, our study encourages bilateral control rather than unilateral control for the risk of predator extinction. |
| format | Article |
| id | doaj-art-cff4084546cf4073a96398effc70519e |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-cff4084546cf4073a96398effc70519e2025-02-03T05:53:22ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/94539419453941Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource ManagementMingzhan Huang0Shouzong Liu1Xinyu Song2Lansun Chen3College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, ChinaCollege of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, ChinaCollege of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, ChinaInstitute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, ChinaIn this paper, mathematical models for the management of biological resources based on a given predator-prey relationship are proposed, and two types of control strategies, unilateral and bilateral control with impulsive state feedback, are studied. The existence of the order-1 homoclinic orbit, order-1 periodic solution, and bifurcation of homoclinic of the unilateral control system are obtained, and the attraction region of this system is also discussed. Besides, sufficient conditions for the existence and stability of the order-1 and order-2 periodic solutions of the bilateral control system are also gained. A series of numerical simulations including bifurcation diagrams of periodic solution are performed, which not only verify the theoretical results we get but also reveal some peculiar dynamical phenomena, such as the appearance of high-order periodic solutions and existence of parameter intervals with drastic order change of periodic solution. By comparing the two management strategies, our study encourages bilateral control rather than unilateral control for the risk of predator extinction.http://dx.doi.org/10.1155/2020/9453941 |
| spellingShingle | Mingzhan Huang Shouzong Liu Xinyu Song Lansun Chen Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource Management Complexity |
| title | Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource Management |
| title_full | Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource Management |
| title_fullStr | Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource Management |
| title_full_unstemmed | Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource Management |
| title_short | Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource Management |
| title_sort | dynamics of unilateral and bilateral control systems with state feedback for renewable resource management |
| url | http://dx.doi.org/10.1155/2020/9453941 |
| work_keys_str_mv | AT mingzhanhuang dynamicsofunilateralandbilateralcontrolsystemswithstatefeedbackforrenewableresourcemanagement AT shouzongliu dynamicsofunilateralandbilateralcontrolsystemswithstatefeedbackforrenewableresourcemanagement AT xinyusong dynamicsofunilateralandbilateralcontrolsystemswithstatefeedbackforrenewableresourcemanagement AT lansunchen dynamicsofunilateralandbilateralcontrolsystemswithstatefeedbackforrenewableresourcemanagement |