AUTHOR=Fakhry Nabaa Hassain , Naji Raid Kamel , Smith? Stacey R. , Haque Mainul 

TITLE=Prey fear of a specialist predator in a tri-trophic food web can eliminate the superpredator

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=8

YEAR=2022

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.963991

DOI=10.3389/fams.2022.963991

ISSN=2297-4687

ABSTRACT=<p>We propose an intraguild predation ecological system consisting of a tri-trophic food web with a fear response for the basal prey and a Lotka–Volterra functional response for predation by both a specialist predator (intraguild prey) and a generalist predator (intraguild predator), which we call the superpredator. We prove the positivity, existence, uniqueness, and boundedness of solutions, determine all equilibrium points, prove global stability, determine local bifurcations, and illustrate our results with numerical simulations. An unexpected outcome of the prey's fear of its specialist predator is the potential eradication of the superpredator.</p>