FN Archimer Export Format
PT J
TI Dynamics of the periodically forced light-limited Droop model
BT 
AF Martinez, Carlos
   MAIRET, Francis
   Bernard, Olivier
AS 1:1;2:1,3;3:1,2;
FF 1:;2:PDG-RBE-BRM-LPBA;3:;
C1 Universite Cote d'Azur, Inria, INRA, CNRS, UPMC Univ Paris 06, BIOCORE team, France
   LOV-UPMC Sorbonne-CNRS, UMR 7093, Station Zoologique, B.P. 28, 06234 Villefranche-sur-mer, France
   IFREMER Physiology and Biotechnology of Algae Laboratory, Nantes, France
C2 INRIA, FRANCE
   CNRS, FRANCE
   IFREMER, FRANCE
SI NANTES
SE PDG-RBE-BRM-LPBA
IN WOS Ifremer UPR
   copubli-france
IF 2.43
TC 3
UR https://archimer.ifremer.fr/doc/00599/71140/69455.pdf
LA English
DT Article
DE ;Variable quota model;Positive periodic solution;Global stability;Microalgae;Cooperative system
AB The periodically forced light-limited Droop model represents microalgae growth under co-limitation 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 sub-homogeneous dynamical systems, we describe the global dynamics of the reduced system. Then, using the theory of asymptotically periodic semiflows, we extend the results on the reduced system to the original model. To illustrate the applicability of the main result, we include an example considering a standard microalgae population model. 
PY 2020
PD AUG
SO Journal Of Differential Equations
SN 0022-0396
PU Elsevier
VL 269
IS 4
UT 000534488300036
BP 3890
EP 3913
DI 10.1016/j.jde.2020.03.020
ID 71140
ER

EF