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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

Dynamics of a Predator-Prey Model with group defense and Exponential Fading Memory

Discontinuity, Nonlinearity, and Complexity 12(3) (2023) 497--510 | DOI:10.5890/DNC.2023.09.003

Prabir Panja

Department of Applied Science, Haldia Institute of Technology, Haldia-721657, West Bengal, India

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Abstract

In this paper, a predator-prey model with Monod-Haldane type functional response is developed. Here, it is assumed that prey grows logistically in the absence of predator. Also, predator population is divided into two subpopulations such as juvenile predator and mature predator respectively. To incorporate the group defense behavior in the model, Monod-Haldane type functional response is considered. It is considered that a portion of juvenile predator becomes mature predator. It is assumed that the growth rate of predator at an instant is not depends only the density of prey at the present time, but also depends on the density of the prey on the previous instant of time. Different possible equilibrium points are determined. Also, the stability of the model around these equilibrium points is studied. Hopf bifurcation analysis of the model is done with respect to some important parameters. It is observed that exponential fading memory has a big role in the stability of the model. Finally, some numerical simulation results have been presented for better understanding of the dynamics of the model.

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