Title: Explosive tritrophic food chain model with herd behaviour of prey and finite time blow-up of the top predator

Authors: Debaldev Jana; G.P. Samanta; Ashok Mondal; Sudeshna Mondal; A.K. Pal; Debasis Manna

Addresses: Department of Mathematics and SRM Research Institute, SRM Institute of Science and Technology, Kattankulathur-603 203, Tamil Nadu, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology,Shibpur, Howrah-711 103, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology,Shibpur, Howrah-711 103, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology,Shibpur, Howrah-711 103, India ' Department of Mathematics, S.A. Jaipuria College, Kolkata-700005, India ' Department of Mathematics, Surendranath Evening College, Kolkata-700 009, India

Abstract: In this work, we have discussed the dynamical behaviours of a three species food chain model where the prey species exhibits herd behaviour and sexually reproductive top predator are of generalist type. Positivity and uniform boundedness of the system are studied to verify its well-posedness. Some conditions for extinction of prey and predators are derived. Feasibility criteria and stability analysis of all the equilibrium points are discussed here. Hopf-bifurcation condition for interior equilibrium point is carried out analytically. Mathematical conditions for finite time blow-up of top predator are established. Numerical simulations are carried out to validate our analytical findings.

Keywords: square root functional response; generalist predator; sexual reproduction; Hopf-bifurcation; finite time blow-up.

DOI: 10.1504/IJDSDE.2022.122524

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.1, pp.36 - 56

Received: 09 Jul 2019
Accepted: 30 Aug 2019
Published online: 03 May 2022 *