The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

Hasan S. Panigoro; Resmawan Resmawan; Emli Rahmi; Muhammad Afrizal Beta; Amelia Tri Rahma Sidik

doi:10.1051/e3sconf/202340003003

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The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

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Hasan S. Panigoro, Resmawan Resmawan, Emli Rahmi, Muhammad Afrizal Beta, Amelia Tri Rahma Sidik

2023 E3S Web of Conferences Vol. 400 Conference paper Cited by 0 SDG 14SDG 16

Abstract

Modeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The analytical results show that the model has two fixed points, namely the origin and the interior points. The possible dynamical behaviors are shown analytically and demonstrated numerically using some phase portraits. We show numerically that the model has limit-cycles on its interior. This guarantees that there exists a condition where both prey and predator maintain their existence periodically. © 2023 The Authors.

Affiliations

Biomathematics Research Group, Universitas Negeri Gorontalo, Bone Bolango, 96554, Indonesia; Department of Mathematics, Universitas Negeri Gorontalo, Bone Bolango, 96554, Indonesia

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