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

R. Ratianingsih*, Fitriani, N. Nacong, Resnawati, Mardlijah, B. Widodo

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationSymposium on Biomathematics, SYMOMATH 2017
EditorsDewi Handayani, Mikkel Quam, Peter van Heijster
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735416291
Publication statusPublished - 6 Mar 2018
Externally publishedYes
EventSymposium on Biomathematics, SYMOMATH 2017 - Bandung, Indonesia
Duration: 27 Aug 201729 Aug 2017

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


ConferenceSymposium on Biomathematics, SYMOMATH 2017


  • Dynamics model
  • Jacobian matrix
  • Microalgae growth model
  • Pontryagin minimal principal


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