E. Abulesz and G. Lyberatos, « Periodic optimization of continuous microbial growth processes, Biotechnology and Bioengineering, 1987.

J. E. Bailey, « Periodic Operations of Chemical Reactors : a Review, Chemical Engineering Communications, 1973.

M. Bardi and I. Capuzzo-dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser, 1997.

L. Barreira and C. Valls, Ordinary Differential Equations : Qualitative Theory, pp.978-0821887493, 2012.

G. Bastin, On Extremum Seeking in Bioprocesses with Multivalued Cost Functions, 2009.

T. Bayen, A. Rapaport, and F. Tani, « Optimal periodic control for scalar dynamics under integral constraint on the input, Mathematical Control and Related Fields, 2019.

T. Bayen, A. Rapaport, and F. Tani, « Improvement of performances of the chemostat used for continuous biological water treatment with periodic controls, Automatica, 2020.

J. Bezanson, A Fresh Approach to Numerical Computing, SIAM Review, 2017.

J. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems, pp.978-979, 2000.

G. , On the choice of the optimal periodic operation for a continuous fermentation process, 2010.

D. Dochain, M. Perrier, and M. Guay, « Extremum seeking control and its application to process and reaction systems : A survey, Mathematics and Computer in Simulation, 2010.

R. Fekih-salem, C. Lobry, and T. Sari, « A density-dependent model of competition for one resource in the chemostat, Mathamtical Biosciences, 2017.

H. I. Freedman and P. Moson, « Persistence Definitions and their Connections, Proceedings of the, 1990.

C. D. De-gooijer, Bioreactors in series : An overview of design procedures and practical applications, Enzyme and Microbial Technology, 1996.

J. Harmand and D. Dochain, « The optimal design of two interconnected (bio)chemical reactors revisited, Computer & Chemical Engineering, 2005.

J. Harmand, théorie mathématique de la culture continue de micro-organismes, pp.978-979, 2017.

M. W. Hirsch, Systems of Differential Equations Which Are Competitive or Cooperative : I. Limit Sets, 1982.

M. W. Hirsch, Systems of Differential Equations Which Are Competitive or Cooperative : II. Convergence Almost Everywhere, 1985.

S. B. Hsu, H. L. Smith, and P. Waltman, « Competitive Exclusion and coexistence for competitive systems on ordered Banach spaces, Transactions of the, 1996.

U. Krause and R. D. Nussbaum, « A Limit Set Trichotomy for Self-Mappings of Normal Cones in Banach Spaces, Nonlinear Analysis, Theory, Methods & Applications, pp.90074-90077, 1993.

R. B. Lovitt and J. W. Wimpenny, « The Gradostat : a Bidirectional Compound Chemostat and Its Application in Microbiological Research, journal of General Microbiology, 1981.

, Thomas Guilmeau -Rapport non-confidentiel

C. Maffezzoni, « Hamilton-Jacobi Theory for Periodic Control Problems, Journal of Optimization Theory and Applications, 1974.

P. De-mottoni and A. Schiaffino, « Competition systems with periodic coefficients : A geometric approach, Journal of Mathematical Biology, 1981.

C. Rackauckas and Q. Nie, « Differentialequations. jl-a performant and feature-rich ecosystem for solving differential equations in julia, Journal of Open Research Software, 2017.

A. Rapaport, D. Dochain, and J. Harmand, « Long run coexistence in the chemostat with multiple species, Journal of Theoretical Biology, 2009.

H. L. Smith, « Cooperative systems of differential equations with concave nonlinearities, Nonlinear Analysis : Theory, Methods & Applications, pp.90087-90095, 1986.

H. L. Smith, « Microbial growth in periodic gradostats, Rocky Mountains Journal of Mathematics, 1990.

H. L. Smith, Monotone dynamical systems : Reflections on new advances & applications ». In : Discrete & Continuous Dynamical Systems, 2017.

H. L. Smith and P. Waltman, The Theory of the Chemostat, dynamics of microbial competition, pp.0-521, 1995.

G. Stephanopoulos and A. G. , Frederickson et R. Aris. « The growth of competing microbial populations in a CSTR with periodically varying inputs, 1979.

, BOCOP : an open source toolbox for optimal control, Inria Saclay Team Commands

. .. , Extremum atteint sur un ensemble non-connexe, p.25

, Comparaison de s(.) et s(?(.))

L. .. , , p.30

, Courbes s m (s), en bleu selon les contraintes, en rouge selon la condition de pente

C. .. De-pente, , p.35

, Le solveur Bocop ne renvoie pas toujours une trajectoire BBSB, p.41

. .. Une-meilleure-façon-d'initialiser-le-solveur-bocop, , p.42

H. .. Résultats-avec-bocop,

B. .. Quatre-cas-de-trajectoires, , p.44

, Un phénomène d'inhibition pour une fonction de croissance de type Hill

, (t)) atteint deux fois son maximum dans le cas non-monotone 47

. .. De-la-compétition, 64 2.3? en bleu, avec µ 1 (.) et µ 2 (.) affines sur [s, s in ], Deux issues possibles, p.69

. .. , suit un régime transitoire contrairement à r(.), p.71

, 2) perturbé pour différentes conditions initiales

C. De-lipschitz-locaux-de and P. .. , , p.75

.. .. Norme-de-p-(x)-?-x,

, Dégradation des performances avec l'installation d'une deuxième espèce convexe

&. .. Schéma-de-principe, , p.79

.. .. Deux-réservoirs-en-série,

. .. Réservoirs-en-série, , p.85

, Convergence vers l'unique solution périodique dans le gradostat en série (2 réservoirs)

, Thomas Guilmeau -Rapport non-confidentiel