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

Bifurkasi Hopf pada Model Lotka-Volterra Orde-Fraksional dengan Efek Allee Aditif pada Predator

Hasan S. Panigoro, Dian Savitri

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.

Keywords

Lotka-Volterra; Additive Allee Effect; Hopf Bifurcation; Fractional-Order

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DOI: https://doi.org/10.34312/jjbm.v1i1.6908

Copyright (c) 2020 Hasan S. Panigoro, Dian Savitri

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