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ISSN:2325-6192 (print)
ISSN:2325-6206 (online)
Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn

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

Journal of Environmental Accounting and Management 11(1) (2023) 1--22 | 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 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.

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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