This article aims to study the dynamics of a Lotka-Volterra predator-prey model with Allee effect in predator; [Bifurkasi Hopf pada Model Lotka-Volterra Orde-Fraksional dengan Efek Allee Aditif pada Predator]

Hasan S. Panigoro; Dian Savitri

doi:10.34312/jjbm.v1i1.6908

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This article aims to study the dynamics of a Lotka-Volterra predator-prey model with Allee effect in predator; [Bifurkasi Hopf pada Model Lotka-Volterra Orde-Fraksional dengan Efek Allee Aditif pada Predator]

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Hasan S. Panigoro, Dian Savitri

2020 Jambura Journal of Biomathematics Vol. 1 Issue 1 Article Cited by 7 SDG 17SDG 14SDG 16

Abstract

This article aims to study the dynamics of a Lotka-Volterra predator-prey model with Allee effect in predator. According to the biological condition, the Caputo fractional-order derivative is chosen as its operator. The analysis is started by identifying the existence, uniqueness, and non-negativity of the solution. Furthermore, the existence of equilibrium points and their stability is investigated. It has shown that the model has two equilibrium points namely both populations extinction point which is always a saddle point, and a conditionally stable co-existence point, both locally and globally. One of the interesting phenomena is the occurrence of Hopf bifurcation driven by the order of derivative. Finally, the numerical simulations are given to validate previous theoretical results. © 2020 by the Authors.

Affiliations

Jurusan Matematika, Universitas Negeri Gorontalo, Gorontalo, 96119, Indonesia; Jurusan Matematika, Universitas Negeri Surabaya, Surabaya, 60231, Indonesia; Jurusan Matematika, Universitas Brawijaya, Malang, 65145, Indonesia

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