The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic Scenarios
In view of a time lag between the time that the prey perceive predator signals and make some changes or behavior responses, we establish a predator–prey system with direct and indirect predation in this paper. First, we investigate the existence, boundedness, and global asymptotical stability of the...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3214358 |
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| _version_ | 1832552941358153728 |
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| author | Weili Kong Yuanfu Shao |
| author_facet | Weili Kong Yuanfu Shao |
| author_sort | Weili Kong |
| collection | DOAJ |
| description | In view of a time lag between the time that the prey perceive predator signals and make some changes or behavior responses, we establish a predator–prey system with direct and indirect predation in this paper. First, we investigate the existence, boundedness, and global asymptotical stability of the positive equilibrium status. Next, by perturbing the mortality rates of prey species and predator species, we stretch the deterministic system to the stochastic scenario and investigate the existence of stochastic process and the global asymptotical stability of the equilibrium status. The analytical findings show that fear affects the value of the equilibrium status, and stochastic disturbance affects its stability, but time delay has no effect if some conditions are satisfied, which are verified by some examples and numerical simulations. |
| format | Article |
| id | doaj-art-bf02c5a0f4764615a650f9d3a74b4cf3 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-bf02c5a0f4764615a650f9d3a74b4cf32025-02-03T05:57:28ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3214358The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic ScenariosWeili Kong0Yuanfu Shao1College of Teacher EducationCollege of ScienceIn view of a time lag between the time that the prey perceive predator signals and make some changes or behavior responses, we establish a predator–prey system with direct and indirect predation in this paper. First, we investigate the existence, boundedness, and global asymptotical stability of the positive equilibrium status. Next, by perturbing the mortality rates of prey species and predator species, we stretch the deterministic system to the stochastic scenario and investigate the existence of stochastic process and the global asymptotical stability of the equilibrium status. The analytical findings show that fear affects the value of the equilibrium status, and stochastic disturbance affects its stability, but time delay has no effect if some conditions are satisfied, which are verified by some examples and numerical simulations.http://dx.doi.org/10.1155/2022/3214358 |
| spellingShingle | Weili Kong Yuanfu Shao The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic Scenarios Journal of Mathematics |
| title | The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic Scenarios |
| title_full | The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic Scenarios |
| title_fullStr | The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic Scenarios |
| title_full_unstemmed | The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic Scenarios |
| title_short | The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic Scenarios |
| title_sort | long time behavior of equilibrium status of a predator prey system with delayed fear in deterministic and stochastic scenarios |
| url | http://dx.doi.org/10.1155/2022/3214358 |
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