GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECT
This paper aims to discover the impact of the fear of predators in prey, Allee effect for predator reproduction and time delay corresponding to the gestation period on the dynamics of a predator- prey model. Existence, non-negativity, and boundedness of the model solutions are guaranteed. The crite...
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University of Zakho
2025-01-01
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| Series: | Science Journal of University of Zakho |
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| Online Access: | http://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/1406 |
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| author | Didar Akram Abdulqadr Arkan Nawzad Mustafa |
| author_facet | Didar Akram Abdulqadr Arkan Nawzad Mustafa |
| author_sort | Didar Akram Abdulqadr |
| collection | DOAJ |
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This paper aims to discover the impact of the fear of predators in prey, Allee effect for predator reproduction and time delay corresponding to the gestation period on the dynamics of a predator- prey model. Existence, non-negativity, and boundedness of the model solutions are guaranteed. The criteria for asymptotically stability of all the biologically feasible steady state points are determined. It is also determined a critical value for time delay, where the model under goes Hopf -bifurcation near coexistence steady state point. Finally, with the help of the MATLAB program, to confirm the analytical results and discover the impact of fear, the Allee effect, and time delay, the model was solved numerically.it is observed that fear affect negatively on both prey and predator species and the time delay may system may induce a transition of the dynamics of system from the a stability situation to the state where the populations oscillate periodically or vice versa
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| format | Article |
| id | doaj-art-20ceedad5a2f45f7b21d4413201fa5b9 |
| institution | Kabale University |
| issn | 2663-628X 2663-6298 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Zakho |
| record_format | Article |
| series | Science Journal of University of Zakho |
| spelling | doaj-art-20ceedad5a2f45f7b21d4413201fa5b92025-01-31T02:39:09ZengUniversity of ZakhoScience Journal of University of Zakho2663-628X2663-62982025-01-0113110.25271/sjuoz.2025.13.1.1406GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECTDidar Akram Abdulqadr0Arkan Nawzad Mustafa1Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq.Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq This paper aims to discover the impact of the fear of predators in prey, Allee effect for predator reproduction and time delay corresponding to the gestation period on the dynamics of a predator- prey model. Existence, non-negativity, and boundedness of the model solutions are guaranteed. The criteria for asymptotically stability of all the biologically feasible steady state points are determined. It is also determined a critical value for time delay, where the model under goes Hopf -bifurcation near coexistence steady state point. Finally, with the help of the MATLAB program, to confirm the analytical results and discover the impact of fear, the Allee effect, and time delay, the model was solved numerically.it is observed that fear affect negatively on both prey and predator species and the time delay may system may induce a transition of the dynamics of system from the a stability situation to the state where the populations oscillate periodically or vice versa http://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/1406FearTime delayAllee effectStability analysisHopf bifurcation |
| spellingShingle | Didar Akram Abdulqadr Arkan Nawzad Mustafa GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECT Science Journal of University of Zakho Fear Time delay Allee effect Stability analysis Hopf bifurcation |
| title | GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECT |
| title_full | GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECT |
| title_fullStr | GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECT |
| title_full_unstemmed | GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECT |
| title_short | GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECT |
| title_sort | global stability and hopf bifurcation of a delayed predator prey model incorporating allee effect and fear effect |
| topic | Fear Time delay Allee effect Stability analysis Hopf bifurcation |
| url | http://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/1406 |
| work_keys_str_mv | AT didarakramabdulqadr globalstabilityandhopfbifurcationofadelayedpredatorpreymodelincorporatingalleeeffectandfeareffect AT arkannawzadmustafa globalstabilityandhopfbifurcationofadelayedpredatorpreymodelincorporatingalleeeffectandfeareffect |