The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource
A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilib...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-04-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/8/865 |
| _version_ | 1827695090524487680 |
|---|---|
| author | Jialin Chen Xiaqing He Fengde Chen |
| author_facet | Jialin Chen Xiaqing He Fengde Chen |
| author_sort | Jialin Chen |
| collection | DOAJ |
| description | A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results. |
| first_indexed | 2024-03-10T12:19:05Z |
| format | Article |
| id | doaj.art-d5696e545409433ba0a335d4e79725c9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:19:05Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d5696e545409433ba0a335d4e79725c92023-11-21T15:38:08ZengMDPI AGMathematics2227-73902021-04-019886510.3390/math9080865The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food ResourceJialin Chen0Xiaqing He1Fengde Chen2College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, ChinaA discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.https://www.mdpi.com/2227-7390/9/8/865discrete predator-prey systemfear effectglobal attractivityother food resource |
| spellingShingle | Jialin Chen Xiaqing He Fengde Chen The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource Mathematics discrete predator-prey system fear effect global attractivity other food resource |
| title | The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource |
| title_full | The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource |
| title_fullStr | The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource |
| title_full_unstemmed | The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource |
| title_short | The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource |
| title_sort | influence of fear effect to a discrete time predator prey system with predator has other food resource |
| topic | discrete predator-prey system fear effect global attractivity other food resource |
| url | https://www.mdpi.com/2227-7390/9/8/865 |
| work_keys_str_mv | AT jialinchen theinfluenceoffeareffecttoadiscretetimepredatorpreysystemwithpredatorhasotherfoodresource AT xiaqinghe theinfluenceoffeareffecttoadiscretetimepredatorpreysystemwithpredatorhasotherfoodresource AT fengdechen theinfluenceoffeareffecttoadiscretetimepredatorpreysystemwithpredatorhasotherfoodresource AT jialinchen influenceoffeareffecttoadiscretetimepredatorpreysystemwithpredatorhasotherfoodresource AT xiaqinghe influenceoffeareffecttoadiscretetimepredatorpreysystemwithpredatorhasotherfoodresource AT fengdechen influenceoffeareffecttoadiscretetimepredatorpreysystemwithpredatorhasotherfoodresource |