Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity

Year 2023, , 65 - 75, 07.08.2023

Debasis Mukherjee

https://doi.org/10.33187/jmsm.1177403

Abstract

This paper analyses a discrete-time Michaelis-Menten type harvested fishery model in the presence of toxicity. Boundary and interior (positive) fixed points are examined. Using an iteration scheme and the comparison principle of difference equations, we determined the sufficient condition for global stability of the interior fixed point. It is shown that the sufficient criterion for Neimark-Sacker bifurcation and flip bifurcation can be established. It is observed that the system behaves in a chaotic manner when a specific set of system parameters is selected, which are controlled by a hybrid control method. Examples are cited to illustrate our conclusions.

Keywords

Bifurcation, Chaos control, Global stability, Michaelis-Menten type harvesting, Toxicity

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