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 |
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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 |