Stability and bifurcation of a time-varying delay predator–prey model with Allee effect, prey refuge and B-D function
This paper mainly considers a time-varying delay predator–prey model with Allee effect, prey refuge and B-D functional response. First, the positivity and boundedness of solutions of such model without delay are proved. Next, the conditions for the existence and local stability of equilibriums are p...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-03-01
|
| Series: | Franklin Open |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2773186324001385 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841556939603968000 |
|---|---|
| author | Qiang Zhou Xin-You Meng |
| author_facet | Qiang Zhou Xin-You Meng |
| author_sort | Qiang Zhou |
| collection | DOAJ |
| description | This paper mainly considers a time-varying delay predator–prey model with Allee effect, prey refuge and B-D functional response. First, the positivity and boundedness of solutions of such model without delay are proved. Next, the conditions for the existence and local stability of equilibriums are provided. The global stability of the system near the positive equilibrium is also obtained by constructing appropriate Lyapunov function. Then, the existence of Hopf bifurcation and the stability of periodic solutions of bifurcation are proved. Furthermore, when the time-varying delay is a periodic function, periodic perturbation is applied to the delay to suppress oscillations by the method of multiple scales, which calculates the amplitude of the perturbation to control oscillations. Finally, the results show that oscillations can be weakened, and numerical simulations are showed to verify our analytical results. |
| format | Article |
| id | doaj-art-5be5c64f947e4a7386f2bd946782a768 |
| institution | Kabale University |
| issn | 2773-1863 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Franklin Open |
| spelling | doaj-art-5be5c64f947e4a7386f2bd946782a7682025-01-07T04:17:39ZengElsevierFranklin Open2773-18632025-03-0110100208Stability and bifurcation of a time-varying delay predator–prey model with Allee effect, prey refuge and B-D functionQiang Zhou0Xin-You Meng1School of Science, Lanzhou University of Technology, Lanzhou, 730050, Gansu, ChinaCorresponding author.; School of Science, Lanzhou University of Technology, Lanzhou, 730050, Gansu, ChinaThis paper mainly considers a time-varying delay predator–prey model with Allee effect, prey refuge and B-D functional response. First, the positivity and boundedness of solutions of such model without delay are proved. Next, the conditions for the existence and local stability of equilibriums are provided. The global stability of the system near the positive equilibrium is also obtained by constructing appropriate Lyapunov function. Then, the existence of Hopf bifurcation and the stability of periodic solutions of bifurcation are proved. Furthermore, when the time-varying delay is a periodic function, periodic perturbation is applied to the delay to suppress oscillations by the method of multiple scales, which calculates the amplitude of the perturbation to control oscillations. Finally, the results show that oscillations can be weakened, and numerical simulations are showed to verify our analytical results.http://www.sciencedirect.com/science/article/pii/S2773186324001385Allee effectTime-varying delayPrey refugeGlobal stability |
| spellingShingle | Qiang Zhou Xin-You Meng Stability and bifurcation of a time-varying delay predator–prey model with Allee effect, prey refuge and B-D function Franklin Open Allee effect Time-varying delay Prey refuge Global stability |
| title | Stability and bifurcation of a time-varying delay predator–prey model with Allee effect, prey refuge and B-D function |
| title_full | Stability and bifurcation of a time-varying delay predator–prey model with Allee effect, prey refuge and B-D function |
| title_fullStr | Stability and bifurcation of a time-varying delay predator–prey model with Allee effect, prey refuge and B-D function |
| title_full_unstemmed | Stability and bifurcation of a time-varying delay predator–prey model with Allee effect, prey refuge and B-D function |
| title_short | Stability and bifurcation of a time-varying delay predator–prey model with Allee effect, prey refuge and B-D function |
| title_sort | stability and bifurcation of a time varying delay predator prey model with allee effect prey refuge and b d function |
| topic | Allee effect Time-varying delay Prey refuge Global stability |
| url | http://www.sciencedirect.com/science/article/pii/S2773186324001385 |
| work_keys_str_mv | AT qiangzhou stabilityandbifurcationofatimevaryingdelaypredatorpreymodelwithalleeeffectpreyrefugeandbdfunction AT xinyoumeng stabilityandbifurcationofatimevaryingdelaypredatorpreymodelwithalleeeffectpreyrefugeandbdfunction |