Dynamical Analysis of a Crowley-Martin Predator-Prey Model with Prey Harvesting and Discrete Time-Delay

The present study deals with the dynamical response of a predator-prey model in which the prey has been subjected to harvesting. The proposed model considers a Crowley-Martin response function which is subjected to Michaelis-Menten type prey harvesting. It is first shown that the system is bounded and the conditions of existence and stability of the equilibria of the proposed model have been furnished. Next the presence of Hopf bifurcation and limit cycles have been shown to explain the transition of the model from a stable to an unstable one. It is seen that harvesting effort has a remarkable effect on the dynamics of the system and can make the system undergo unstability by reaching beyond a critical value. Considering the discrete time delay as bifurcating parameters, the conditions for existence of limit cycle under which the system admits a Hopf-bifurcation are investigated. The detailed study for direction of Hopf-bifurcation have been derived with the use of both the normal form and the central manifold theory.(c) 2023 L&H Scientific Publishing, LLC. All rights reserved.