Study of Fear Effect on Prey–Predator Model with Ivlev-Type Functional Response in Fuzzy Environment

Soumya Das, Suvankar Biswas and Pritha Das
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Soumya Das: Department of Mathematics, Indian Institute of Engineering, Science and Technology, Shibpur, B. Garden, Howrah 711103, India
Suvankar Biswas: ��Mathematics Discipline, School of Sciences, Indira Gandhi National Open University, New Delhi 110068, India
Pritha Das: Department of Mathematics, Indian Institute of Engineering, Science and Technology, Shibpur, B. Garden, Howrah 711103, India

New Mathematics and Natural Computation (NMNC), 2022, vol. 18, issue 03, 715-745

Abstract: A prey–predator model with Ivlev-type functional response and the fear effect on prey species by the predator have been considered for the first time in a crisp as well as fuzzy environment. The effects of fear have been investigated on the stability of the system. Granular function derivative concept has been used to do fuzzy mathematics. For the first time, proper model analysis, positivity, bounds and uniform persistence are studied for our proposed model in fuzzy environment. The conditions of stability of all co-existing equilibrium points and Hopf bifurcation analysis have also been studied in fuzzy environment. Analytical results have been justified by numerical simulation with proper table and graphical presentation in crisp and fuzzy environment both.

Keywords: Prey–predator model; fuzzy number; granular function derivative; fear effect; Ivlev-type functional response; stability analysis; Hopf bifurcation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S1793005722500351

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