Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour
This paper is devoted to studying the dynamics of a delayed reaction-diffusion predator–prey system incorporating the effects of fear and anti-predator behaviour. First, based on its mathematical model, the global attractor is analyzed and the local stability of its positive equilibria is derived. M...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3270 |
| _version_ | 1797485235869319168 |
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| author | Zhenglong Chen Shunjie Li Xuebing Zhang |
| author_facet | Zhenglong Chen Shunjie Li Xuebing Zhang |
| author_sort | Zhenglong Chen |
| collection | DOAJ |
| description | This paper is devoted to studying the dynamics of a delayed reaction-diffusion predator–prey system incorporating the effects of fear and anti-predator behaviour. First, based on its mathematical model, the global attractor is analyzed and the local stability of its positive equilibria is derived. Moreover, the Hopf bifurcation induced by the time delay variable is also investigated. Furthermore, the existence and non-existence of non-constant positive solutions are analyzed. Finally, numerical simulations are presented to validate the theoretical analysis. |
| first_indexed | 2024-03-09T23:15:52Z |
| format | Article |
| id | doaj.art-ad6c29aa681e4f6dabae17b5f97e2919 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:52Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ad6c29aa681e4f6dabae17b5f97e29192023-11-23T17:35:41ZengMDPI AGMathematics2227-73902022-09-011018327010.3390/math10183270Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator BehaviourZhenglong Chen0Shunjie Li1Xuebing Zhang2School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaSchool of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaSchool of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaThis paper is devoted to studying the dynamics of a delayed reaction-diffusion predator–prey system incorporating the effects of fear and anti-predator behaviour. First, based on its mathematical model, the global attractor is analyzed and the local stability of its positive equilibria is derived. Moreover, the Hopf bifurcation induced by the time delay variable is also investigated. Furthermore, the existence and non-existence of non-constant positive solutions are analyzed. Finally, numerical simulations are presented to validate the theoretical analysis.https://www.mdpi.com/2227-7390/10/18/3270predator–prey systemfear effectanti-predator behaviourHopf bifurcationdiffusion |
| spellingShingle | Zhenglong Chen Shunjie Li Xuebing Zhang Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour Mathematics predator–prey system fear effect anti-predator behaviour Hopf bifurcation diffusion |
| title | Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour |
| title_full | Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour |
| title_fullStr | Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour |
| title_full_unstemmed | Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour |
| title_short | Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour |
| title_sort | analysis of a delayed reaction diffusion predator prey system with fear effect and anti predator behaviour |
| topic | predator–prey system fear effect anti-predator behaviour Hopf bifurcation diffusion |
| url | https://www.mdpi.com/2227-7390/10/18/3270 |
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