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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

Impact of Predator Induced Fear in a Predator-Prey Model where Predator Species Suffers from Cannibalism

Discontinuity, Nonlinearity, and Complexity 13(2) (2024) 291--303 | DOI:10.5890/DNC.2024.06.007

Narayan Mondal, Dipesh Barman, Shariful Alam

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B.Garden, Howrah, 711103, India

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Abstract

In this article, a prey-predator model has been proposed considering predator induced fear to prey species. Furthermore, it is considered that predator species suffers from cannibalism. It is observed that both the parameter associated with predator induced fear and cannibalism play a crucial role in controlling the stability of system dynamics. The predator induced fear factor acts as a stabilizing factor while predator cannibalism phenomenon affects the system dynamics in absence of fear through the occurrence of multiple local bifurcations; but in presence of fear factor this cannibalism act cannot influence system dynamics. On the other hand, it is noticed that predator's birth rate due to cannibalism plays as a stable factor in system dynamics for a suitable range of this parameter. Additionally, it is observed that there is an important relationship between the phenomenon fear and cannibalism. Both the phenomenon individually affects the population biomass in a significant way.

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