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Digital Object Identifier (DOI): 10.1007/s002850200160

Summary: Digital Object Identifier (DOI):
J. Math. Biol. 45, 313­336 (2002)
Mathematical Biology
Julien Arino · Jean-Luc Gouz´e · Antoine Sciandra
A discrete, size-structured model of phytoplankton
growth in the chemostat
Introduction of inhomogeneous cell division size
Received: 9 February 2000 / Revised version: 10 October 2001 /
Published online: 23 August 2002 ­ c Springer-Verlag 2002
Abstract. We introduce inhomogeneous, substrate dependent cell division in a time discrete,
nonlinear matrix model of size-structured population growth in the chemostat, first intro-
duced by Gage et al. [8] and later analysed by Smith [13]. We show that mass conservation
is verified, and conclude that our system admits one non zero globally stable equilibrium,
which we express explicitly. Then we run numerical simulations of the system, and compare
the predictions of the model to data related to phytoplankton growth, whose obtention we
discuss. We end with the identification of several parameters of the system.
A chemostat is a continuous culture device in which organisms (bacteria, phyto-
plankton) grow, submitted to a flow of nutrient. Chemostats have been extensively


Source: Arino, Julien - Department of Mathematics, University of Manitoba
Sciandra, Antoine - Laboratoire d'Oceanographie de Villefranche


Collections: Environmental Sciences and Ecology; Geosciences; Mathematics