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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

Fear Effect in a Tri-Trophic Food Chain Model with Holling Type IV Functional Response

Journal of Environmental Accounting and Management 9(3) (2021) 235--253 | DOI:10.5890/JEAM.2021.09.004

Krishnendu Sarkar$^{1}$, Nijamuddin Ali$^{2}$, Lakshmi Narayan Guin$^{1}$

$^{1}$ Department of Mathematics, Visva-Bharati, Santiniketan 731235, India

$^{2}$ Department of Mathematics, Vivekananda Mahavidyalaya, Purba Bardhaman, West Bengal, 713103, India

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Abstract

Of concern the present study deals with an updated food chain model comprising one prey and two predator species in a natural environment with the inclusion of fear effect in both the prey and the median predator population through Holling type IV functional response. The present model is affluent with intra-specific competition among the hunter species having specific mortality. The model system emphasizes its characteristics in the proximity of the probable equilibrium position in the realm of biological dynamics. The response of the system is explored further for its stability analysis based on prerequisites and Hopf-bifurcation phenomena as well with respect to some significant model parameters. A quantitative analysis based on numerical simulation is also carried out in order to validate the analytical results and thereby the applicability of the model is established.

Acknowledgments

The authors would like to express thank the anonymous referees and the editors for making productive remarks and suggestions in order to improve the quality of the work done. The first and third authors gratefully acknowledge 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)). We are grateful to Prof. Santabrata Chakravarty, Department of Mathematics, Visva-Bharati, Santiniketan-731235, West Bengal, India for comments on an earlier version of the manuscript.

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