Journal of Environmental Accounting and Management
Dynamical Analysis of a CrowleyMartin PredatorPrey Model with Prey Harvesting and Discrete TimeDelay
Journal of Environmental Accounting and Management 11(1) (2023) 122
 DOI:10.5890/JEAM.2023.03.001
Anindita Bhattacharyya$^1$,
Ashok Mondal$^2$, Sanghita Bose$^1$, A. K. Pal$^3$
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Abstract
The present study deals with the dynamical response of a predatorprey model in which the prey has been subjected to harvesting. The proposed model considers a CrowleyMartin response function which is subjected to MichaelisMenten 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 Hopfbifurcation are investigated. The detailed study for direction of Hopfbifurcation have been derived with the use of both the normal form and the central manifold theory.
Acknowledgments
The authors are grateful to the anonymous referees and the
Associate Editor (Prof. Dimitri Volchenkov) for their careful reading, valuable comments and helpful suggestion, which have helped them to improve the presentation of this work significantly.
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