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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

Dynamics of a Predator-prey Model with Beddington-DeAngelis Functional Response, Omnivory and Predator Switching

Journal of Vibration Testing and System Dynamics 5(4) (2021) 407--428 | DOI:10.5890/JVTSD.2021.12.006

Prabir Panja

Department of Applied Science, Haldia Institute of Technology, Purba Midnapore-721657, W.B., India

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Abstract

In this paper, a predator-prey model has been developed by considering Beddington-DeAngelis functional response among the interaction of three species prey, middle predator and top predator. It is assumed that middle predator consumes only prey, but top predator consumes prey as well as middle predator. The concept of omnivory has been introduced in this model. Also, it is assumed that due to omnivory property, the top predator has a chance to prefer the food (prey) to consume. Here two types of predator switching behavior such as preferential switching and density dependent switching have been introduced. Different possible equilibrium points are evaluated and the stability of the system has been investigated around these points. Theoretical analysis of for the existence condition of Hopf bifurcation of the system has been studied with respect to $w_4$. It is found that the increase of death rate of middle and top predator may be responsible for the extinction of both the species or that particular species. It is observed that omnivory may lead the system towards stability. It is also observed that the predator switching behaviour may strengthen the stability and persistence of all populations. Finally, some numerical simulation results have been presented to validate the analytical findings.

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