Title: Harvesting in tri-trophic food chain stabilises the chaotic dynamics-conclusion drawn from Hastings and Powell model

Authors: Binayak Nath; Krishna Pada Das

Addresses: Department of Physics, Mahadevananda Mahavidyalaya, Monirampore, P.O.-Barrackpore, Kolkata 700120, India ' Department of Mathematics, Mahadevananda Mahavidyalaya, Monirampore, P.O.-Barrackpore, Kolkata 700120, India

Abstract: The paper explores a tri-trophic food chain model with harvesting in the species. The curiosity of this paper is to observe chaotic dynamics and its control. We perform the local stability analysis of the equilibrium points. The Hopf bifurcation analysis and global stability around the interior equilibrium point are also performed. Our numerical simulations reveal that the three species food chain model induces chaos from period-doubling, limit cycle and stable focus for increasing values of half saturation constant. We conclude that chaotic dynamics can be controlled by the harvesting parameter. We apply basic tools of non-linear dynamics such as Poincare section and Lyapunov exponent to identify chaotic behaviour of the system.

Keywords: harvesting; chaos; stable focus; Poincare map; Lyapunov exponent; persistence; Hopf bifurcation.

DOI: 10.1504/IJDSDE.2020.106025

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.2, pp.95 - 115

Received: 01 Dec 2017
Accepted: 12 Aug 2018
Published online: 25 Mar 2020 *

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