Bifurcation analysis of a mathematical model of microalgae growth under the influence of sunlight

Mahardhika, Lingga Sanjaya Putra and Adi-Kusumo, Fajar and Ertiningsih, Dwi (2023) Bifurcation analysis of a mathematical model of microalgae growth under the influence of sunlight. Biomath, 12 (1): 2301307. ISSN 1314684X

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Abstract

In this paper is considered a microalgae growth model under the influence of sunlight. The model is a two-dimensional system of the first order Ordinary Differential Equations (ODE) with a ten-dimensional parameter space. For this model, we study the existence of equilibrium points and their stability, and determine a bifurcation of the system when the value of some parameters is varied. The Lambert ! function is used to calculate equilibrium points and apply the linearization technique to provide their stabilities. By varying the value of some parameters numerically, we found a transcritical bifurcation of the system and show stability regions of the equilibrium points in parameter diagrams. The bifurcation shows that the microalgae have a minimum sustainable nutrition supply and have a minimum light intensity that plays an important role for survival in a chemostat which has a certain depth. The results can be used to design a chemostat in optimizing the growth of microalgae

Item Type: Article
Additional Information: Library Dosen
Uncontrolled Keywords: Microalgae growth model, Quota cell, Parameter diagram, Bifurcation
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Mathematics and Natural Sciences > Mathematics Department
Depositing User: Masrumi Fathurrohmah
Date Deposited: 10 Jul 2024 07:23
Last Modified: 10 Jul 2024 07:23
URI: https://ir.lib.ugm.ac.id/id/eprint/2511

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