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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

Stability and Bifurcation Analysis of a Delay Induced Modified Leslie-Gower Predator-Prey Model with Generalised Holling type-II Response Function and Fear Effect

Journal of Environmental Accounting and Management 12(4) (2024) 389--418 | DOI:10.5890/JEAM.2024.12.005

Ashok Mondal$^1$, A. K. Pal$^2$

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Abstract

In this article, we investigate a modified Leslie-Gower predator-prey system with generalised Holling Type-II functional response together with fear effect in prey. The model is extended by incorporating two constant time delays, where the first delay is for density dependent feedback mechanism in the logistic growth of the prey and the second one is for gestation delay of the predator population. The dynamical behaviours such as boundedness, extinction criteria and existence, stability and bifurcations of the equilibria of the non-delay model are qualitatively discussed. The existence of periodic solutions via Hopf-bifurcation with respect to both delays is set up. Finally, numerical simulations have been carried out to confirm our numerical findings.

Acknowledgments

The authors are grateful to the anonymous referees and the Editor (Prof. Jiazhong Zhang) 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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