Bifurcation Analysis of Food Chain with Release of Fear, Additional Food and Anti-predator Behavior for the Top Predator Species

Saba Majeed; Rana Noori  Majeed

doi:10.30526/39.4.4416

Authors

Saba Noori Majeed Computer Department, College of Education for Women, University of Baghdad, Baghdad, Iraq. https://orcid.org/0000-0003-1590-0055
Rana Noori Majeed Department of Mathematics, College of Education for Pure Science (Ibn Al Haitham), University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-2643-0231

DOI:

https://doi.org/10.30526/39.4.4416

Keywords:

food chain , bifurcation

Abstract

This paper investigates the bifurcation analysis of a three-species food chain model with a Holling type II functional response, focusing on the effect of fear and additional food on both middle and top predators, respectively, accompanied by the presence of anti-predatory behavior. The system boundedness had been proven, the existence of all the equilibrium under certain conditions examined, the local stability of the system’s equilibrium point demonstrated, and local and Hopf bifurcations have been proved with certain determinations according to specific parameters included in the food chain model. The theoretical results of the system were simulated numerically with phase diagrams to assure local stability at a specific set of the parameters' values with time series for the included populations. Furthermore, the system's bifurcations were verified around the interior equilibrium point during growth parameter versus prey population, creating saddle-node bifurcation, as well as top predator versus predation parameter through Hopf bifurcation. Finally, the conclusion presents the most important results and future recommendations that were submitted

Author Biographies

Saba Noori Majeed, Computer Department, College of Education for Women, University of Baghdad, Baghdad, Iraq.

Computer Department -
Rana Noori Majeed, Department of Mathematics, College of Education for Pure Science (Ibn Al Haitham), University of Baghdad, Baghdad, Iraq

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