@article{fdi:010084511,
  title = {{C}oupling of bio-reactors to increase maximum sustainable yield},
  author = {{A}uger, {P}ierre and {M}oussaoui, {A}.},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n the field of fisheries management, the objective is to obtain an optimal catch while maintaining the fishery resource at a sufficiently high level to avoid the extinction of the exploited species. {I}n mathematical fishery models, the fishing effort that must be implemented to have a sustainable fishery with a maximum harvest rate in the long term is sought. {T}his goal is called the "{M}aximum {S}ustainable {Y}ield" ({MSY}). {I}n the chemostat, the substrate can be seen as prey of which the predator is the product. {MSY} search is thus extended to the classical chemostat model with a {M}onod function. {T}here exists a dilution rate that maximizes the product synthesis. {T}he study is extended to the case of the gradostat with fast substrate and product exchanges between two coupled bioreactors. {T}he existence of two time scales makes it possible to apply methods of aggregation of variables to derive a reduced model governing a few global variables describing the dynamics of the complete system at the slow time scale. {T}he analysis of the mathematical aggregated model is performed. {E}xistence of equilibria as well as local and global stability are studied. {T}he overall product yield in the system of coupled bioreactors may be greater than the sum of the yields of the two uncoupled bioreactors, i.e., if they functioned without connection between them. {T}he increase in product yield is all the more important as the distribution of the substrate and of the product is asymmetrical between the two coupled bioreactors. {T}he model is applied to fish farming by considering the coupling of two breeding sites. {H}ere again, the model makes it possible to find the fast fish exchanges that must be established between the two breeding basins to optimize the overall yield of the farm.},
  keywords = {bioreactor ; maximum sustainable yield ; fast substrate and product ; exchanges ; aggregation of variables ; global stability of equilibria ; gradostat ; fish farming},
  booktitle = {},
  journal = {{M}athematics},
  volume = {10},
  numero = {4},
  pages = {555 [18 p.]},
  year = {2022},
  DOI = {10.3390/math10040555},
  URL = {https://www.documentation.ird.fr/hor/fdi:010084511},
}