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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Predator-Prey Model with Intraguild Predation in an Uncertain Environment

Journal of Vibration Testing and System Dynamics 7(4) (2023) 399--417 | DOI:10.5890/JVTSD.2023.12.001

Prabir Panja, Sailen Gayen, Dipak Kumar Jana

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

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Abstract

In this paper, a prey, intermediate predator and top predator interaction model has been developed. Here all parameters of the model have been considered as triangular fuzzy number. Positivity and boundedness of solutions of the proposed model have been investigated. Possible equilibrium points of the model are determined and also local stability of the model around these equilibrium points have been studied. Global stability of the model around the interior equilibrium point is also studied. Conditions for the existence of Hopf bifurcation have been investigated with respect to $\alpha$ (degree of uncertainty). It is found that the uncertain values of the parameters have a great influence in the solution of the proposed model. From the analysis of the model, it is observed that intra-species competition rate of prey as well as intermediate predator can be stabilized the system. It is also observed that the harvesting rate of intermediate predator has the ability to stabilize the system. Some complex behaviour of the system have been seen due to the increase of death rate of top predator species. Finally some numerical simulation results have been presented to verify the analytical findings.

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