The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior

Hanna Rasool Hadi; Azhar  Abbas Majeed

doi:10.30526/38.1.3598

Authors

Hanna Rasool Hadi Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq. https://orcid.org/0009-0007-7885-1840
Azhar Abbas Majeed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq. https://orcid.org/0000-0002-9652-6132

DOI:

https://doi.org/10.30526/38.1.3598

Keywords:

Prey-Predator, Local Bifurcation, Global Bifurcation, Sotomayor's theorem

Abstract

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.

Author Biographies

Hanna Rasool Hadi, Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.

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Azhar Abbas Majeed, Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.

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