D. Ami, P. Cartigny, and A. Rapaport, Can marine protected areas enhance both economic and biological situations?, Comptes Rendus Biologies, vol.328, issue.4, pp.357-366, 2005.
DOI : 10.1016/j.crvi.2004.10.018

URL : https://hal.archives-ouvertes.fr/hal-00999802

W. Bakker, H. Beeftink, C. De-gooijer, and J. Tramper, Bioreactors in series: An overview of design procedures and practical applications, Enzyme and Microbial Technology, vol.18, pp.202-219, 1996.

M. Bardi and I. , Capuzzo-Dolcetta, Optimal Control and Visosity Solutions of Hamilton-Jacobi- Bellman Equations, 1997.

T. Bayen, F. Mairet, and P. Gajardo, Optimal Synthesis for the Minimum Time Control Problems of Fed-Batch Bioprocesses for Growth Functions with Two Maxima, Journal of Optimization Theory and Applications, vol.11, issue.11, pp.521-553, 2013.
DOI : 10.1007/s10957-012-0225-0

URL : https://hal.archives-ouvertes.fr/hal-01088417

B. Bonnard and M. Chyba, Singular Trajectories and their role in Control Theory, p.40, 2002.

U. Boscain and B. Piccoli, Optimal Syntheses for Control Systems on 2-D Manifolds, 2004.

P. Cadarliaguet, On the Regularity of Semipermeable Surfaces in Control Theory with Application to the Optimal Exit-Time Problem (Part I), SIAM Journal on Control and Optimization, vol.35, issue.5, pp.1638-1652, 1997.
DOI : 10.1137/S0363012995287295

P. Cadarliaguet, On the Regularity of Semipermeable Surfaces in Control Theorywith Application to the Optimal Exit-Time Problem (Part II), SIAM Journal on Control and Optimization, vol.35, issue.5, pp.1653-1671, 1997.
DOI : 10.1137/S0363012996312155

C. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources., Biometrics, vol.49, issue.2, 1990.
DOI : 10.2307/2532591

I. Cacciari, S. Grego, and E. D. Mattia, Eco-physiological characterization of soil bacterial populations in different states of growth, Microb. Ecol, vol.43, issue.1, pp.34-43, 2002.

C. Camarasa, T. Clement, M. Perez, J. R. Mouret, and J. M. Sablayrolles, Use of a continuous multistage bioreactor to mimic winemaking fermentation, International Journal of Food Microbiology, vol.150, issue.1, pp.42-49, 2011.

D. Dochain and A. Rapaport, Minimal time control of fed-batch processes for growth functions with several maxima, IEEE Transactions on Automatic Control, vol.56, pp.11-2671, 2011.

A. Dramé, J. Harmand, C. Lobry, and A. Rapaport, Multiple steady state profiles in interconnected biological systems, Mathematical and Computer Modelling of Dynamical Systems, vol.75, issue.5, pp.379-393, 2006.
DOI : 10.1080/13873950600723277

B. Dubey, P. Chandra, and P. Sinha, A model for fishery resource with reserve area, Nonlinear Analysis: Real World Applications, vol.4, issue.4, pp.625-637, 2003.
DOI : 10.1016/S1468-1218(02)00082-2

B. Bonnard, J. Caillau, and E. Trélat, Second order optimality conditions in the smooth case and applications in optimal control, ESAIM: Control, Optimisation and Calculus of Variations, vol.13, issue.2, pp.207-236, 2007.
DOI : 10.1051/cocv:2007012

URL : https://hal.archives-ouvertes.fr/hal-00086380

D. Dochain and P. Vanrolleghem, Dynamical Modelling & Estimation in Wastewater Treatment Processes, Water Intelligence Online, vol.4, issue.0, 2001.
DOI : 10.2166/9781780403045

H. El-owaidy and O. El-leithy, Theoretical studies on extinction in the gradostat, Mathematical Biosciences, vol.101, issue.1, pp.1-26, 1990.
DOI : 10.1016/0025-5564(90)90099-K

P. Gajardo, H. Ramirez, and A. Rapaport, Minimal Time Sequential Batch Reactors with Bounded and Impulse Controls for One or More Species, SIAM Journal on Control and Optimization, vol.47, issue.6, pp.2827-2856, 2008.
DOI : 10.1137/070695204

URL : https://hal.archives-ouvertes.fr/hal-00857823

F. Gérard, I. Haidar, and A. Rapaport, Effects of spatial structure and diffusion on the performances of the chemostat, Mathematical Biosciences and Engineering, vol.8, issue.4, pp.953-971, 2011.

R. Hannesson and M. Reserves, Marine Reserves: What Would They Accomplish?, Marine Resource Economics, vol.13, issue.3, pp.159-170, 1998.
DOI : 10.1086/mre.13.3.42629231

J. Harmand, A. Rapaport, and A. Trofino, Optimal design of interconnected bioreactors: New results, AIChE Journal, vol.70, issue.6, pp.1433-1450, 1999.
DOI : 10.1002/aic.690490609

Y. Higashi, N. Ytow, H. Saida, and H. Seki, In situ gradostat for the study of natural phytoplankton community with an experimental nutrient gradient Environmental Pollution, pp.99-395, 1998.

G. Hill and C. Robinson, Minimum tank volumes for CFST bioreactors in series, The Canadian Journal of Chemical Engineering, vol.52, issue.5, pp.818-824, 1989.
DOI : 10.1002/cjce.5450670513

E. B. Lee and L. Markus, Foundations of optimal control theory, 1967.

U. Ledzewicz and H. Schattler, Geometric Optimal Control, 2012.

R. Lovitt and J. Wimpenny, The Gradostat: a Bidirectional Compound Chemostat and its Application in Microbiological Research, Microbiology, vol.127, issue.2, pp.261-268, 1981.
DOI : 10.1099/00221287-127-2-261

A. Miele, Application of Green's Theorem to the extremization of linear integrals, Symp. on Vehicle Systems Optimization, pp.26-35, 1961.

K. Mischaikow, H. L. Smith, and H. , Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions, Transactions of the American Mathematical Society, vol.347, issue.5, pp.1669-1685, 1995.
DOI : 10.1090/S0002-9947-1995-1290727-7

J. A. Moreno, Optimal time control of bioreactors for the wastewater treatment, Optimal Control Applications and Methods, vol.20, issue.3, pp.145-164, 1999.
DOI : 10.1002/(SICI)1099-1514(199905/06)20:3<145::AID-OCA651>3.0.CO;2-J

M. Nelson and H. Sidhu, Evaluating the performance of a cascade of two bioreactors, Chemical Engineering Science, vol.61, issue.10, pp.61-3159, 2006.
DOI : 10.1016/j.ces.2005.12.007

M. Quincampoix, Differential Inclusions and Target Problems, SIAM Journal on Control and Optimization, vol.30, issue.2, pp.324-335, 1992.
DOI : 10.1137/0330020

J. A. Sanchirico and J. E. Wilen, Bioeconomics of Spatial Exploitation in a Patchy Environment, Journal of Environmental Economics and Management, vol.37, issue.2, pp.129-144, 1999.
DOI : 10.1006/jeem.1998.1060

H. L. Smith and P. Waltman, The gradostat: A model of competition along a nutrient gradient, Microbial Ecology, vol.1, issue.1, pp.207-226, 1991.
DOI : 10.1007/BF02540224

H. L. Smith and P. Waltman, The theory of the chemostat, Dynamics of microbial competition, 1995.

B. Tang, Mathematical investigations of growth of microorganisms in the gradostat, Journal of Mathematical Biology, vol.297, issue.3, pp.319-339, 1986.
DOI : 10.1007/BF00275252

H. Veldcamp, Ecological Studies with the Chemostat, Advances in Microbial Ecology, vol.1, pp.59-95, 1977.
DOI : 10.1007/978-1-4615-8219-9_2