W. Allee, Animal Aggregations, The Quarterly Review of Biology, vol.2, issue.3, 1931.
DOI : 10.1086/394281

R. Brammer, Controllability in Linear Autonomous Systems with Positive Controllers, SIAM Journal on Control, vol.10, issue.2, p.339, 1972.
DOI : 10.1137/0310026

A. Fillipov, Differential equations with discontinuous righthand sides, 1988.
DOI : 10.1007/978-94-015-7793-9

F. Grognard and J. Gouzé, POSITIVE CONTROL OF LOTKA-VOLTERRA SYSTEMS, Proceedings of 16th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.00724

URL : https://hal.archives-ouvertes.fr/hal-01091732

B. A. Hawkins and H. V. Cornell, Theoretical Approaches to Biological Control, 1999.
DOI : 10.1017/CBO9780511542077

M. Kot, Elements of mathematical ecology, 2001.
DOI : 10.1017/CBO9780511608520

M. Meza, A. Bhaya, E. Kaszkurewicz, M. Da-silveira, and . Costa, Threshold policies control for predator???prey systems using a control Liapunov function approach, Theoretical Population Biology, vol.67, issue.4, pp.273-284, 2005.
DOI : 10.1016/j.tpb.2005.01.005

S. Muratori and S. Rinaldi, Structural properties of controlled population models, Systems & Control Letters, vol.10, issue.3, pp.147-153, 1988.
DOI : 10.1016/0167-6911(88)90045-X

M. Rosenzweig, Paradox of Enrichment: Destabilization of Exploitation Ecosystems in Ecological Time, Science, vol.171, issue.3969, p.385, 1971.
DOI : 10.1126/science.171.3969.385

S. Saperstone and J. Yorke, Controllability of Linear Oscillatory Systems Using Positive Controls, SIAM Journal on Control, vol.9, issue.2, pp.253-262, 1971.
DOI : 10.1137/0309019

W. G. Bibliographie1, H. I. Aiello, J. Freedman, and . Wu, Analysis of a model representing stagestructured population growth with state-dependent time delay, SIAM Journal on Applied Mathematics, vol.52, issue.3, pp.855-869, 1992.

V. Andersen and P. Nival, A pelagic ecosystem model simulating production and sedimentation of biogenic particles: role of salps and copepods, Marine Ecology Progress Series, vol.44, issue.1, pp.37-50, 1988.
DOI : 10.3354/meps044037

J. Arino, Modélisation structurée de la croissance du phytoplancton en chemostat, 2001.

J. Arino and J. Gouzé, A size-structured, non-conservative ODE model of the chemostat, Mathematical Biosciences, vol.177, issue.178, pp.127-145, 2002.
DOI : 10.1016/S0025-5564(02)00084-6

S. Ayata, M. Lévy, O. Aumont, A. Sciandra, J. Sainte-marie et al., Phytoplankton growth formulation in marine ecosystem models: Should we take into account photo-acclimation and variable stoichiometry in oligotrophic areas?, Journal of Marine Systems, vol.125
DOI : 10.1016/j.jmarsys.2012.12.010

URL : https://hal.archives-ouvertes.fr/hal-00820981

N. Bacaër, A short history of mathematical population dynamics, 2011.
DOI : 10.1007/978-0-85729-115-8

E. Benoît, Systèmes lents-rapides dans R 3 et leurs canards, Troisième rencontre du Schnepfenried, pp.159-191, 1983.

E. Benoît and M. J. Rochet, A continuous model of biomass size spectra governed by predation and the effects of fishing on them, Journal of Theoretical Biology, vol.226, issue.1, pp.9-21, 2004.
DOI : 10.1016/S0022-5193(03)00290-X

A. Berman, M. Neumann, and R. J. Stern, Nonnegative matrices in dynamic systems, 1989.

T. R. Birkhead, K. E. Lee, and P. Young, Sexual Cannibalism in the Praying Mantis Hierodula Membranacea, Behaviour, vol.106, issue.1, pp.112-118, 1988.
DOI : 10.1163/156853988X00115

R. F. Brammer, Controllability in Linear Autonomous Systems with Positive Controllers, SIAM Journal on Control, vol.10, issue.2, p.339, 1972.
DOI : 10.1137/0310026

À. Calsina and J. Saldaña, A model of physiologically structured population dynamics with a nonlinear individual growth rate, Journal of Mathematical Biology, vol.33, issue.4, pp.335-364, 1995.
DOI : 10.1007/BF00176377

D. Claessen, L. Am-de-roos, and . Persson, Population dynamic theory of sizedependent cannibalism, Proceedings of the Royal Society of London. Series B : Biological Sciences, pp.333-340, 1537.

D. Claessen and A. M. De-roos, Bistability in a size-structured population model of cannibalistic fish???a continuation study, Theoretical Population Biology, vol.64, issue.1, pp.49-65, 2003.
DOI : 10.1016/S0040-5809(03)00042-X

D. Claessen, C. Van-oss, A. M. De-ross, and L. Persson, THE IMPACT OF SIZE-DEPENDENT PREDATION ON POPULATION DYNAMICS AND INDIVIDUAL LIFE HISTORY, Ecology, vol.83, issue.6, pp.1660-1675, 2002.
DOI : 10.1146/annurev.es.15.110184.002141

S. Datta, A mathematical analysis of marine size spectra, 2011.

S. Datta, G. W. Delius, and R. Law, A Jump-Growth Model for Predator???Prey Dynamics: Derivation and Application to Marine Ecosystems, Bulletin of Mathematical Biology, vol.35, issue.3, 2008.
DOI : 10.1007/s11538-009-9496-5

O. Diekmann, A beginners guide to adaptive dynamics, Banach Center publications, vol.63, pp.47-86, 2004.

O. Diekmann, M. Gyllenberg, J. Metz, S. Nakaoka, and A. De-roos, Daphnia revisited: local stability and bifurcation theory for physiologically structured population models explained by way of an example, Journal of Mathematical Biology, vol.3, issue.2, pp.277-318, 2010.
DOI : 10.1007/s00285-009-0299-y

A. Mark, D. R. Elgar, and . Nash, Sexual cannibalism in the garden spider araneus diadematus, Animal Behaviour, vol.36, issue.5, pp.1511-1517, 1988.

K. J. Engel, R. Nagel, S. Brendle, T. Hahn, G. Metafune et al., One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics, 1999.

Z. Jozsef, T. Farkas, and . Hagen, Linear stability and positivity results for a generalized size-structured daphnia model with inflow, Applicable Analysis, vol.86, issue.9, pp.1087-1103, 2007.

Z. Jozsef, T. Farkas, and . Hagen, Stability and regularity results for a sizestructured population model, Journal of Mathematical Analysis and Applications, vol.328, issue.1, pp.119-136, 2007.

K. J. Flynn, A mechanistic model for describing dynamic multi-nutrient, light, temperature interactions in phytoplankton, Journal of Plankton Research, vol.23, issue.9, pp.977-997, 2001.
DOI : 10.1093/plankt/23.9.977

F. Gallucci and E. Ólafsson, Cannibalistic behaviour of rock-pool copepods: An experimental approach for space, food and kinship, Journal of Experimental Marine Biology and Ecology, vol.342, issue.2, pp.325-331, 2007.
DOI : 10.1016/j.jembe.2006.11.004

C. García-comas, L. Stemmann, F. Ibanez, L. Berline, M. G. Mazzocchi et al., Zooplankton long-term changes in the NW Mediterranean Sea: Decadal periodicity forced by winter hydrographic conditions related to large-scale atmospheric changes?, Journal of Marine Systems, vol.87, issue.3-4, pp.3-4216, 2011.
DOI : 10.1016/j.jmarsys.2011.04.003

G. Gorsky, M. D. Ohman, M. Picheral, S. Gasparini, L. Stemmann et al., Digital zooplankton image analysis using the ZooScan integrated system, Journal of Plankton Research, vol.32, issue.3, pp.285-303, 2010.
DOI : 10.1093/plankt/fbp124

B. Hansen, P. Bjornsen, and P. Hansen, The size ratio between planktonic predators and their prey, Limnology and Oceanography, vol.39, issue.2, pp.395-403, 1994.
DOI : 10.4319/lo.1994.39.2.0395

A. Bradford, H. V. Hawkins, and . Cornell, Theoretical Approaches to Biological Control, 1999.

J. Hofbauer and K. Sigmund, Evolutionary games and population dynamics, 1998.
DOI : 10.1017/CBO9781139173179

F. Jiménez, J. Rodríguez, B. Bautista, and V. Rodríguez, Relations between chlorophyll, phytoplankton cell abundance and biovolume during a winter bloom in Mediterranean coastal waters, Journal of Experimental Marine Biology and Ecology, vol.105, issue.2-3, pp.2-3161, 1987.
DOI : 10.1016/0022-0981(87)90169-9

C. Kaewmanee and I. M. Tang, Cannibalism in an age-structured predator???prey system, Ecological Modelling, vol.167, issue.3, pp.213-220, 2003.
DOI : 10.1016/S0304-3800(03)00190-X

C. Kohlmeier and W. Ebenhöh, The stabilizing role of cannibalism in a predator-prey system, Bulletin of Mathematical Biology, vol.118, issue.3, pp.401-411, 1995.
DOI : 10.1007/BF02460632

S. A. Koo?man, Dynamic Energy and Mass Budgets in Biological Systems, 2000.

M. Kot, Elements of mathematical ecology, 2001.
DOI : 10.1017/CBO9780511608520

Y. Kuang and H. I. Freedman, Uniqueness of limit cycles in Gause-type models of predator-prey systems, Mathematical Biosciences, vol.88, issue.1, pp.67-84, 1988.
DOI : 10.1016/0025-5564(88)90049-1

G. Lacroix and M. Grégoire, Revisited ecosystem model (MODECOGeL) of the Ligurian Sea: seasonal and interannual variability due to atmospheric forcing, Journal of Marine Systems, vol.37, issue.4, pp.229-258, 2002.
DOI : 10.1016/S0924-7963(02)00190-2

P. H. Leslie, ON THE USE OF MATRICES IN CERTAIN POPULATION MATHEMATICS, Biometrika, vol.33, issue.3, pp.183-212, 1945.
DOI : 10.1093/biomet/33.3.183

W. Liu, D. Xiao, and Y. Yi, Relaxation oscillations in a class of predator???prey systems, Journal of Differential Equations, vol.188, issue.1, pp.306-331, 2003.
DOI : 10.1016/S0022-0396(02)00076-1

G. Kjartan and . Magnússon, Destabilizing effect of cannibalism on a structured predatorprey system, Mathematical Biosciences, vol.155, issue.1, pp.61-75, 1999.

O. Maury, B. Faugeras, Y. Shin, J. Poggiale, T. B. Ari et al., Modeling environmental effects on the size-structured energy flow through marine ecosystems. Part 1: The model, Progress in Oceanography, vol.74, issue.4, pp.479-499, 2007.
DOI : 10.1016/j.pocean.2007.05.002

URL : https://hal.archives-ouvertes.fr/hal-01186904

A. G. Mckendrick, Applications of Mathematics to Medical Problems, Proceedings of the Edinburgh Mathematical Society, pp.98-130, 1926.
DOI : 10.1038/104660a0

J. H. Nichols and A. B. Thompson, Mesh selection of copepodite and nauplius stages of four calanoid copepod species, Journal of Plankton Research, vol.13, issue.3, pp.661-671, 1991.
DOI : 10.1093/plankt/13.3.661

R. E. Malley, Singular perturbation methods for ordinary differential equations. Applied mathematical sciences, 1991.

S. Rinaldi and S. Muratori, Slow-fast limit cycles in predator-prey models, Ecological Modelling, vol.61, issue.3-4, pp.287-308, 1992.
DOI : 10.1016/0304-3800(92)90023-8

S. Rinaldi and S. Muratori, Slow-fast limit cycles in predator-prey models, Ecological Modelling, vol.61, issue.3-4, pp.287-308, 1992.
DOI : 10.1016/0304-3800(92)90023-8

M. Rosenzweig and R. Macarthur, Graphical Representation and Stability Conditions of Predator-Prey Interactions, The American Naturalist, vol.97, issue.895, pp.209-223, 1963.
DOI : 10.1086/282272

S. H. Saperstone, Global Controllability of Linear Systems with Positive Controls, SIAM Journal on Control, vol.11, issue.3, pp.417-423, 1973.
DOI : 10.1137/0311034

L. Hal, P. Smith, and . Waltman, The Theory of the Chemostat : Dynamics of Microbial Competition (Cambridge Studies in Mathematical Biology), 2008.

H. R. Thieme, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, Journal of Mathematical Biology, vol.30, issue.7, pp.755-763, 1992.

S. Tuljapurkar and H. Caswell, Structured-population models in marine, terrestrial, and freshwater systems, 1997.
DOI : 10.1007/978-1-4615-5973-3

P. Vandromme, L. Stemmann, L. Berline, S. Gasparini, L. Mousseau et al., Inter-annual fluctuations of zooplankton communities in the Bay of Villefranche-sur-mer from 1995 to 2005 (Northern Ligurian Sea, France), Biogeosciences, vol.8, issue.11, pp.3143-3158, 1995.
DOI : 10.5194/bg-8-3143-2011

P. Vandromme, Evolution décennale du zooplancton de la mer ligure en relation avec les fluctuations environnementales. De l'imagerie à la modélisation basée en taille, 2010.

P. Vandromme, L. Stemmann, C. Garcia-comas, L. Berline, X. Sund et al., Assessing biases in computing size spectra of automatically classified zooplankton from imaging systems

V. Volterra, Variations and Fluctuations of the Number of Individuals in Animal Species living together, Animal Ecology, 1926.
DOI : 10.1093/icesjms/3.1.3

W. W. Jean-chesson, P. L. Murdoch, and . Chesson, Biological control in theory and practice, The American Naturalist, vol.125, issue.3, pp.344-366, 1985.