Bifurcation analysis of a mathematical model of microalgae growth under the influence of sunlight
DOI:
https://doi.org/10.55630/j.biomath.2023.01.307Keywords:
Microalgae growth model, Quota cell, Parameter diagram, BifurcationAbstract
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 w 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.
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Copyright (c) 2023 Lingga Sanjaya Putra Mahardhika, Fajar Adi-Kusumo, Dwi Ertiningsih
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