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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Incorporating Prey Refuge in a Prey-Predator Model with Beddington-DeAngelis Type Functional Response: A Comparative Study on Intra-Specific Competition

Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 395--419 | DOI:10.5890/DNC.2020.09.005

Hafizul Molla$^{1}$, Md. Sabiar Rahman$^{2}$, Sahabuddin Sarwardi$^{3}$

$^{1}$ Department of Mathematics, Manbhum Mahavidyalaya, Purulia - 723 131, West Bengal, India

$^{2}$ Department of Mathematics, Gobordanga Hindu College, North 24 Parganas -743 273, West Bengal, India

$^{3}$ Department of Mathematics & Statistics, Aliah University, IIA/27, New Town, Kolkata - 700 160, India

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Abstract

The present study deals with a prey-predator system with prey refuge depending on both species with the Beddington-DeAngelis response function. We propose a mathematical model for predator-prey interactions, allowing prey refuge in the absence of intra-specific competition and in the presence of intra-specific competition among the predators. We have analyzed the models in terms of boundedness, persistence, existence of equilibria and their stability and Hopf bifurcation. Existence of paradox of enrichments are examined well in both the cases. The analytical findings of this study are substantially validated by sufficient numerical simulations. The ecological implications of the obtained results are discussed as well.

Acknowledgments

The corresponding author Dr. Sarwardi is thankful to the Department of Mathematics & Statistics, Aliah University, for providing opportunities to perform the present work.

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