The stability analysis of the nutrition restricted dynamic model of the microalgae biomass growth

Abstract

The biomass production is very essential in microalgae farming such that its growth rate is very important to be determined. This paper proposes the dynamics model of it that restricted by its nutrition. The model is developed by considers some related processes that are photosynthesis, respiration, nutrition absorption, stabilization, lipid synthesis and CO₂ mobilization. The stability of the dynamical system that represents the processes is analyzed using the Jacobian matrix of the linearized system in the neighborhood of its critical point. There is a lipid formation threshold needed to require its existence. In such case, the absorption rate of respiration process has to be inversely proportional to the absorption rate of CO₂ due to photosynthesis process. The Pontryagin minimal principal also shows that there are some requirements needed to have a stable critical point, such as the rate of CO₂ released rate, due to the stabilization process that is restricted by 50%, and the threshold of its shifted critical point. In case of the rate of CO₂ released rate due to the photosynthesis process is restricted in such interval; the stability of the model at the critical point could not be satisfied anymore. The simulation shows that the external nutrition plays a role in glucose formation such that sufficient for the biomass growth and the lipid production.