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Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 585--604 | DOI:10.5890/DNC.2021.12.001

Anindita Bhattacharyya$^1$, Sanghita Bose$^1$, Ashok Mondal$^2$, A. K. Pal$^3$

$^{1}$ Department of Mathematics, Amity University, Kolkata-700 135, India

$^2$ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah- 711 103, India

$^3$ Department of Mathematics, Seth Anandram Jaipuria College, Kolkata-700 005, India

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Abstract

The present study deals with the dynamical response of a two-prey one-predator model inculcating the anti-predator fear effect. The proposed model considers a Holling type II response function and it is intended to investigate the effect of the presence of fear among preys due to a predator. It is first shown that the system is bounded and the conditions of existence and stability of the equilibria of the proposed model have been furnished. Next the presence of Hopf bifurcation and limit cycles have been shown to explain the transition of the model from a stable to an unstable one. The study reveals that along with fear the interaction between the preys and predator can also be effectively stated as a control factor in determining dynamics of the model. The effect of anti-predator fear and mutual interaction between the preys and predator has been numerically simulated in order to potray the dynamics of the model and the occurrence of limit cycles.

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