




Martinez, Carlos; Mairet, Francis; Bernard, Olivier. 
The periodically forced lightlimited Droop model represents microalgae growth under colimitation by light and a single substrate, accounting for periodic fluctuations of factors such as light and temperature. In this paper, we describe the global dynamics of this model, considering general monotone growth and uptake rate functions. Our main result gives necessary and sufficient conditions for the existence of a positive periodic solution (i.e. a periodic solution characterized by the presence of microalgae) which is globally attractive. In our approach, we reduce the model to a cooperative planar periodic system. Using results on periodic Kolmogorov equations and on monotone subhomogeneous dynamical systems, we describe the global dynamics of the... 
Tipo: Text 
Palavraschave: Variable quota model; Positive periodic solution; Global stability; Microalgae; Cooperative system. 
Ano: 2020 
URL: https://archimer.ifremer.fr/doc/00599/71140/69455.pdf 
 

 

 


Martinez, Carlos; Mairet, Francis; Plaza, Luis; Sciandra, Antoine; Bernard, Olivier. 
The main resources limiting microalgae growth are typically phosphorus, nitrogen, and light. Based on the theory of the light limited chemostat, the variable cell quota approach, and photoacclimation models, we build a mathematical model for describing microalgae growth under limitation by these resources. The model is calibrated with a data set from the literature. Then, by numerical simulations, we find that under constant operation of the culture and constant environmental conditions (illumination, temperature, pH, etc.), solutions of the model approach towards either a positive or an extinction steady state. Based on the positive steady state, and in the context of wastewater treatment, we evaluate the capacity of microalgae to remove contaminants. We... 
Tipo: Text 
Palavraschave: Control; Biotechnology; Wastewater treatment; Microalgae; Cell quota model. 
Ano: 2019 
URL: https://archimer.ifremer.fr/doc/00600/71188/69541.pdf 
 


Martinez, Carlos; Mairet, Francis; Bernard, Olivier. 
Microalgae can be cultivated in closed or open photobioreactors (PBR). In these systems, light rapidly decreases as it passes through the culture due to the turbidity of the medium. Thus, microalgae experiment different light intensities depending on their position in the medium. In this paper, we study theoretically how the growth rate of microalgae is affected by different factors; incident light intensity, form of the PBR, microalgae population density, turbidity of nonmicroalgae components, and light pathlength of the reactor. We show that for different types of PBR the average growth rate is completely determined by the incident light intensity and the optical depth. In the case of vertical cylindrical PBRs illuminated from above (e.g. raceway or... 
Tipo: Text 
Palavraschave: Photobioreactor; Optical depth; Photoinhibition; Light limitation; Turbidity; Modelling. 
Ano: 2018 
URL: https://archimer.ifremer.fr/doc/00450/56133/57675.pdf 
 


