Dynamic analysis of a predator-prey impulse model with action threshold depending on the density of the predator and its rate of change
The concept of an action threshold that depends on predator density and the rate of change is relatively novel and can engender new ideas among scholars studying predator-prey systems more effectively than earlier concepts. On this basis, a predator-prey system with an action threshold based on pred...
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| Format: | Article |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2024520?viewType=HTML |
| _version_ | 1797245004082577408 |
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| author | Liping Wu Zhongyi Xiang |
| author_facet | Liping Wu Zhongyi Xiang |
| author_sort | Liping Wu |
| collection | DOAJ |
| description | The concept of an action threshold that depends on predator density and the rate of change is relatively novel and can engender new ideas among scholars studying predator-prey systems more effectively than earlier concepts. On this basis, a predator-prey system with an action threshold based on predator density and its change rate has been established and its dynamic behavior studied. The exact phase set and pulse set of the model were obtained conducting image analysis. The Poincaré map of the model has been constructed and the extreme value points, monotonic interval and immobility points of the Poincaré map have been studied. In addition, the nature of the periodic solution is discussed and we present simulations of the interesting dynamical behavior of the model through the use of numerical examples. An action threshold that depends on the density and rate of change of predators is more reasonable and realistic than techniques proposed in earlier studies, which is significant for the study of control strategies. It is the analytical approach adopted in this paper that allows researchers to explore other generalized predator-prey models more fully and in-depth. |
| first_indexed | 2024-04-24T19:20:00Z |
| format | Article |
| id | doaj.art-bba927f4a32d468b996d8c934f64a4e3 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T19:20:00Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-bba927f4a32d468b996d8c934f64a4e32024-03-26T01:32:06ZengAIMS PressAIMS Mathematics2473-69882024-03-0195106591067810.3934/math.2024520Dynamic analysis of a predator-prey impulse model with action threshold depending on the density of the predator and its rate of changeLiping Wu 0Zhongyi Xiang11. School of Mathematics and Statistics, Hubei Minzu University, Enshi 445000, Hubei, China1. School of Mathematics and Statistics, Hubei Minzu University, Enshi 445000, Hubei, China 2. Hubei Key Laboratory of Biologic Resources Protection and Utilization, Hubei Minzu University, Enshi 445000, Hubei, ChinaThe concept of an action threshold that depends on predator density and the rate of change is relatively novel and can engender new ideas among scholars studying predator-prey systems more effectively than earlier concepts. On this basis, a predator-prey system with an action threshold based on predator density and its change rate has been established and its dynamic behavior studied. The exact phase set and pulse set of the model were obtained conducting image analysis. The Poincaré map of the model has been constructed and the extreme value points, monotonic interval and immobility points of the Poincaré map have been studied. In addition, the nature of the periodic solution is discussed and we present simulations of the interesting dynamical behavior of the model through the use of numerical examples. An action threshold that depends on the density and rate of change of predators is more reasonable and realistic than techniques proposed in earlier studies, which is significant for the study of control strategies. It is the analytical approach adopted in this paper that allows researchers to explore other generalized predator-prey models more fully and in-depth.https://aimspress.com/article/doi/10.3934/math.2024520?viewType=HTMLpoincaré mapnonlinear thresholdstate-dependent impulsive systemperiodic solution |
| spellingShingle | Liping Wu Zhongyi Xiang Dynamic analysis of a predator-prey impulse model with action threshold depending on the density of the predator and its rate of change AIMS Mathematics poincaré map nonlinear threshold state-dependent impulsive system periodic solution |
| title | Dynamic analysis of a predator-prey impulse model with action threshold depending on the density of the predator and its rate of change |
| title_full | Dynamic analysis of a predator-prey impulse model with action threshold depending on the density of the predator and its rate of change |
| title_fullStr | Dynamic analysis of a predator-prey impulse model with action threshold depending on the density of the predator and its rate of change |
| title_full_unstemmed | Dynamic analysis of a predator-prey impulse model with action threshold depending on the density of the predator and its rate of change |
| title_short | Dynamic analysis of a predator-prey impulse model with action threshold depending on the density of the predator and its rate of change |
| title_sort | dynamic analysis of a predator prey impulse model with action threshold depending on the density of the predator and its rate of change |
| topic | poincaré map nonlinear threshold state-dependent impulsive system periodic solution |
| url | https://aimspress.com/article/doi/10.3934/math.2024520?viewType=HTML |
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