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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 Stage Structured Predator-prey Model with Fear Effects

Discontinuity, Nonlinearity, and Complexity 11(4) (2022) 651--669 | DOI:10.5890/DNC.2022.12.007

Prabir Panja

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

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Abstract

In this article, a predator-prey model has been developed incorporating two important factors, namely, the fear factor and the stage structure on both species. It is considered that the growth rate of the prey population is suppressed due to the fear of adult predators. Two separate compartments such as prey and dead prey of prey population have been considered. Also, predator population has been classified into three subpopulations such as suckling in predator population, juvenile and adult predator population. Different possible biologically meaningful equilibrium points are evaluated. Local stability of our proposed system around these equilibrium points has been investigated. Global stability of the interior equilibrium point has also been studied. Hopf bifurcation analysis of the system around the interior equilibrium point with respect to fear factor $(k)$ has been investigated. Direction and stability of Hopf bifurcation are also investigated. It is found that the fear factor has the ability to stabilize the system. It is also found that the higher rate of consumption of dead prey by juvenile and adult predator may make the system unstable. Again, it is also found that the rate of transfer of predator from suckling stage to juvenile stage can change the system dynamics. Some numerical simulation results are presented to validate analytical findings.

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