The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior
In this paper, the conditions under which the occurrence of the local bifurcation (such as saddle-node (SN), transcritical (TC), and pitchfork (PT)) of all stable points of a food web model have been investigated. Fear and anti-predator responses involving the Holling-type IV and Growly-Martin...
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University of Baghdad
2025-01-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
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| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3598 |
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| author | Hanna Rasool Hadi Azhar Abbas Majeed |
| author_facet | Hanna Rasool Hadi Azhar Abbas Majeed |
| author_sort | Hanna Rasool Hadi |
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In this paper, the conditions under which the occurrence of the local bifurcation (such as saddle-node (SN), transcritical (TC), and pitchfork (PT)) of all stable points of a food web model have been investigated. Fear and anti-predator responses involving the Holling-type IV and Growly-Martin functional responses have been found. It has been shown that there are transcritical and pitchfork bifurcations near H3, H4, and H6 as well as a saddle-node bifurcation close to the positive equilibrium point. In addition, there is a saddle-node bifurcation in close to the positive equilibrium point. These divergences have materialised into existence. In conclusion, To prove that the analytical results are correct, a numerical simulation of a set of parameters and starting conditions has been used.
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| format | Article |
| id | doaj-art-23f8b4fa72ec498198d589e3ad41d9a4 |
| institution | Kabale University |
| issn | 1609-4042 2521-3407 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj-art-23f8b4fa72ec498198d589e3ad41d9a42025-01-22T01:21:06ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072025-01-0138110.30526/38.1.3598The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behaviorHanna Rasool Hadi0https://orcid.org/0009-0007-7885-1840Azhar Abbas Majeed1https://orcid.org/0000-0002-9652-6132Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq. In this paper, the conditions under which the occurrence of the local bifurcation (such as saddle-node (SN), transcritical (TC), and pitchfork (PT)) of all stable points of a food web model have been investigated. Fear and anti-predator responses involving the Holling-type IV and Growly-Martin functional responses have been found. It has been shown that there are transcritical and pitchfork bifurcations near H3, H4, and H6 as well as a saddle-node bifurcation close to the positive equilibrium point. In addition, there is a saddle-node bifurcation in close to the positive equilibrium point. These divergences have materialised into existence. In conclusion, To prove that the analytical results are correct, a numerical simulation of a set of parameters and starting conditions has been used. https://jih.uobaghdad.edu.iq/index.php/j/article/view/3598Prey-PredatorLocal BifurcationGlobal BifurcationSotomayor's theorem |
| spellingShingle | Hanna Rasool Hadi Azhar Abbas Majeed The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior Ibn Al-Haitham Journal for Pure and Applied Sciences Prey-Predator Local Bifurcation Global Bifurcation Sotomayor's theorem |
| title | The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior |
| title_full | The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior |
| title_fullStr | The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior |
| title_full_unstemmed | The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior |
| title_short | The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior |
| title_sort | local bifurcation of food web prey predator model involving fear and anti predator behavior |
| topic | Prey-Predator Local Bifurcation Global Bifurcation Sotomayor's theorem |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3598 |
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