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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

Dynamic Response of Allee Effect and Refuge on the Interacting Species Model System

Journal of Environmental Accounting and Management 11(2) (2023) 193--224 | DOI:10.5890/JEAM.2023.06.006

Lakshmi Narayan Guin, Deepabali Datta, Santabrata Chakravarty

Department of Mathematics, Visva-Bharati, Santiniketan-731 235, West Bengal, India

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Abstract

The present concern is to explore the complexity of the dynamics of a Leslie-Gower predator-prey model with the inclusion of the Allee effect and a constant proportion of prey refuge. Due attention is paid on the non-negativity, dissipativity, uniform boundedness and permanence of the dynamical system as well. Theoretical investigation is carried out on the existence of feasible equilibria of the system followed by the deductions imperative for the conditions of stability of the interior equilibrium. The analysis corresponding to the global stability of equilibrium using a suitable Lyapunov function is, however, not ruled out from the present pursuit. Moreover, the analytical conditions for the occurrence of bifurcation phenomena are ascertained both for a saddle-node bifurcation and a Hopf bifurcation. Numerical simulations are implemented finally at the end in order to validate the theoretical outcomes together with the concluding remarks relevant to the biological implications.

Acknowledgments

The authors are thankful to the anonymous referees and the Editor, Journal of Environmental Accounting and Management (JEAM), L \& H Scientific Publishing, LLC for their careful reading, valuable comments, and helpful suggestions, which have helped us to improve the presentation of this research work significantly. 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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