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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

Effect of Prey Refuge in a Three Species Food Chain Model with Beddington-DeAngelis Functional Response

Journal of Environmental Accounting and Management 11(2) (2023) 139--160 | DOI:10.5890/JEAM.2023.06.002

Lakshmi Narayan Guin$^{1}$, Sriparna Nandi$^{1}$, Santabrata Chakravarty$^{2}$

$^{1}$ Department of Mathematics, Visva-Bharati, Santiniketan-731 235, West Bengal, India, Telefax: +913463261029

$^{2}$ Former Professor, Department of Mathematics, Visva-Bharati, Santiniketan-731 235, West Bengal, India

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Abstract

The present theoretical investigation concerns itself with a three-species food chain model of the Beddington-DeAngelis variety paying special attention to prey refuge. The analytical treatment yields different conditions for the existence of ecologically feasible equilibria. The local stability analysis is carried out for these equilibria from analytical point of view while their global performance is numerically simulated for an ecologically meaningful choice of parameters. Special emphasis is put on the dynamics of bifurcation of the system fashioned by prey refuge parameter. The numerical simulations reveal that the present food chain model with constant prey refuge prevails upon limit cycle from the stable scenario to reduce the refuge parameter value. This observation supports one to conclude that the prey refuge parameter plays a significant role in controlling the dynamics of bifurcation of the system under consideration.

Acknowledgments

All the authors are grateful to the anonymous referees and the Editor, Journal of Environmental Accounting and Management (JEAM), L \& H Scientific Publishing, LLC for their watchful reading, introductory remarks, and supportive ideas, which have helped us develop the presentation of this research work a lot. The first author gratefully acknowledges the financial support in part from Special Assistance Programme (SAP-III) sponsored by the University Grants Commission (UGC), New Delhi, India (Grant No. F.$510$ / $3$ / DRS-III / $2015$ (SAP-I)).

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