P. Abrams and L. E. Katz, Metabolic eects of obesity causing disease in childhood, Case 2 If ? FM ? ? FM ? 1, then System (A.3) has only one steady state, p.2327, 2011.

M. B. Allison and M. G. Myers, 20 YEARS OF LEPTIN: Connecting leptin signaling to biological function, Journal of Endocrinology, vol.223, issue.1, pp.25-35, 2014.
DOI : 10.1530/JOE-14-0404

S. S. Alpert, A two-reservoir energy model of the human body. The American journal of clinical nutrition, p.17101718, 1979.

P. Arner and K. L. Spalding, Fat cell turnover in humans, Biochemical and Biophysical Research Communications, vol.396, issue.1, p.101104, 2010.
DOI : 10.1016/j.bbrc.2010.02.165
URL : https://hal.archives-ouvertes.fr/hal-00372715

R. L. Atkinson, Current status of the eld of obesity, Trends in Endocrinology & Metabolism, vol.25, issue.6, p.283284, 2014.

A. S. Banks, S. M. Davis, S. H. Bates, and M. G. Myers, Activation of Downstream Signals by the Long Form of the Leptin Receptor, Journal of Biological Chemistry, vol.275, issue.19, p.2751456314572, 2000.
DOI : 10.1074/jbc.275.19.14563

W. A. Banks, The many lives of leptin, Peptides, vol.25, issue.3, p.331338, 2004.
DOI : 10.1016/j.peptides.2004.02.014

W. A. Banks, C. M. Clever, and C. L. Farrell, Partial saturation and regional variation in the blood-to-brain transport of leptin in normal weight mice, American Journal of Physiology -Endocrinology and Metabolism, issue.6, pp.278-1158, 2000.

W. A. Banks, A. B. Coon, S. M. Robinson, A. Moinuddin, J. M. Shultz et al., Triglycerides Induce Leptin Resistance at the Blood-Brain Barrier, Diabetes, vol.53, issue.5, p.5312531260, 2004.
DOI : 10.2337/diabetes.53.5.1253

W. A. Banks, C. R. Dipalma, and C. L. Farrell, Impaired transport of leptin across the blood-brain barrier in obesity???, Peptides, vol.20, issue.11, p.2013411345, 1999.
DOI : 10.1016/S0196-9781(99)00139-4

W. A. Banks and C. L. Farrell, Impaired transport of leptin across the blood-brain barrier in obesity is acquired and reversible, American Journal of Physiology - Endocrinology And Metabolism, vol.285, issue.1, pp.10-15, 2003.
DOI : 10.1152/ajpendo.00468.2002

W. A. Banks, A. J. Kastin, W. Huang, J. B. Jaspan, and L. M. Maness, Leptin enters the brain by a saturable system independent of insulin, Peptides, vol.17, issue.2, p.305311, 1996.
DOI : 10.1016/0196-9781(96)00025-3

G. S. Barsh, I. S. Farooqi, O. Rahilly, and S. , Genetics of body-weight regulation, Nature, issue.6778, p.404644651, 2000.

B. Beck, N. Musse, and A. Stricker-krongrad, Ghrelin, Macronutrient Intake and Dietary Preferences in Long???Evans Rats, Biochemical and Biophysical Research Communications, vol.292, issue.4, p.10311035, 2002.
DOI : 10.1006/bbrc.2002.6737

B. D. Bennett, G. P. Solar, J. Q. Yuan, J. Mathias, G. R. Thomas et al., A role for leptin and its cognate receptor in hematopoiesis, Current Biology, vol.6, issue.9, p.11701180, 1996.
DOI : 10.1016/S0960-9822(02)70684-2

C. Bjørbaek, H. J. Lavery, S. H. Bates, R. K. Olson, S. M. Davis et al., SOCS3 Mediates Feedback Inhibition of the Leptin Receptor via Tyr985, Journal of Biological Chemistry, vol.275, issue.51, p.2754064940657, 2000.
DOI : 10.1074/jbc.M007577200

C. Bjørbaek, S. Uotani, B. Da-silva, and J. S. Flier, Divergent Signaling Capacities of the Long and Short Isoforms of the Leptin Receptor, Journal of Biological Chemistry, vol.272, issue.51, p.2723268632695, 1997.
DOI : 10.1074/jbc.272.51.32686

I. Brady and K. D. Hall, Dispatch from the eld: is mathematical modeling applicable to obesity treatment in the real world? Obesity, p.19391941, 2014.

G. A. Bray, Eect of caloric restriction on energy expenditure in obese patients, Lancet, issue.27617, p.397398, 1969.

L. A. Campeld and F. J. Smith, Transient declines in blood glucose signal meal initiation, International Journal of Obesity, vol.14, issue.314, p.1531, 1990.

C. C. Chow and K. D. Hall, The Dynamics of Human Body Weight Change, PLoS Computational Biology, vol.332, issue.2, pp.1000045-173, 2008.
DOI : 10.1371/journal.pcbi.1000045.g003

C. C. Chow and K. D. Hall, Short and long-term energy intake patterns and their implications for human body weight regulation, Physiology & Behavior, vol.134, p.6065, 2014.
DOI : 10.1016/j.physbeh.2014.02.044

C. Cobelli, G. Toolo, and E. Ferrannini, A model of glucose kinetics and their control by insulin, compartmental and noncompartmental approaches, Mathematical Biosciences, vol.72, issue.2, pp.291-315, 1984.
DOI : 10.1016/0025-5564(84)90114-7

M. Covasa, Decits in gastrointestinal responses controlling food intake and body weight, American Journal of Physiology -Regulatory, Integrative and Comparative Physiology, issue.6, pp.299-1423, 2010.

D. E. Cummings, Ghrelin and the short- and long-term regulation of appetite and body weight, Physiology & Behavior, vol.89, issue.1, p.7184, 2006.
DOI : 10.1016/j.physbeh.2006.05.022

D. E. Cummings and M. H. Shannon, Roles for ghrelin in the regulation of appetite and body weight, Archives of Surgery, vol.138, issue.4, p.389396, 2003.

A. A. De-graaf, A. P. Freidig, B. D. Roos, N. Jamshidi, M. Heinemann et al., Nutritional Systems Biology Modeling: From Molecular Mechanisms to Physiology, PLoS Computational Biology, vol.8, issue.2, p.1000554, 2009.
DOI : 10.1371/journal.pcbi.1000554.g004

A. M. Depaoli, 20 YEARS OF LEPTIN: Leptin in common obesity and associated disorders of metabolism, Journal of Endocrinology, vol.223, issue.1, pp.71-81, 2014.
DOI : 10.1530/JOE-14-0258

E. Doucet, S. St-pierre, N. Alméras, J. P. Després, C. Bouchard et al., Evidence for the existence of adaptive thermogenesis during weight loss, British Journal of Nutrition, vol.17, issue.06, p.715723, 2001.
DOI : 10.1530/eje.0.1350659

F. A. Duca and M. Covasa, Current and emerging concepts on the role of peripheral signals in the control of food intake and development of obesity, British Journal of Nutrition, vol.278, issue.05, p.778793, 2012.
DOI : 10.1016/j.acthis.2010.09.007
URL : https://hal.archives-ouvertes.fr/hal-01190725

F. A. Duca, L. Zhong, and M. Covasa, Reduced CCK signaling in obese-prone rats fed a high fat diet, Hormones and Behavior, vol.64, issue.5, p.812817, 2013.
DOI : 10.1016/j.yhbeh.2013.09.004
URL : https://hal.archives-ouvertes.fr/hal-01204282

A. G. Dulloo and J. Jacquet, Adaptive reduction in basal metabolic rate in response to food deprivation in humans: a role for feedback signals from fat stores, The American journal of clinical nutrition, issue.3, p.68599606, 1998.

K. El-haschimi, D. D. Pierroz, S. M. Hileman, C. Bjørbaek, and J. S. Flier, Two defects contribute to hypothalamic leptin resistance in mice with diet-induced obesity. The journal of clinical investigation, p.10518271832, 2000.

J. K. Elmquist, C. F. Elias, and C. B. Saper, From Lesions to Leptin, Neuron, vol.22, issue.2, p.221232, 1999.
DOI : 10.1016/S0896-6273(00)81084-3

J. Erdmann, F. Lippl, S. Wagenpfeil, and V. Schusdziarra, Dierential association of basal and postprandial plasma ghrelin with leptin, insulin, and type 2 diabetes, Diabetes, issue.5, p.5413711378, 2005.

J. Erdmann, R. Töpsch, F. Lippl, P. Gussmann, and V. Schusdziarra, Postprandial Response of Plasma Ghrelin Levels to Various Test Meals in Relation to Food Intake, Plasma Insulin, and Glucose, The Journal of Clinical Endocrinology & Metabolism, vol.89, issue.6, p.8930483054, 2004.
DOI : 10.1210/jc.2003-031610

S. A. Evans, A. D. Parsons, and J. M. Overton, Homeostatic responses to caloric restriction: influence of background metabolic rate, Journal of Applied Physiology, vol.99, issue.4, p.13361342, 2005.
DOI : 10.1152/japplphysiol.01380.2004

I. S. Farooqi, O. Rahilly, and S. , 20 YEARS OF LEPTIN: Human disorders of leptin action, Journal of Endocrinology, vol.223, issue.1, pp.63-70, 2014.
DOI : 10.1530/JOE-14-0480

J. S. Flier, Obesity Wars, Cell, vol.116, issue.2, p.337350, 2004.
DOI : 10.1016/S0092-8674(03)01081-X

G. B. Forbes, Lean Body Mass-Body Fat Interrelationships in Humans, Nutrition Reviews, vol.45, issue.10, p.45225231, 1987.
DOI : 10.1111/j.1753-4887.1987.tb02684.x

J. Friedman, 20 YEARS OF LEPTIN: Leptin at 20: an overview, Journal of Endocrinology, vol.223, issue.1, pp.1-8, 2014.
DOI : 10.1530/JOE-14-0405

J. M. Friedman, Leptin, Leptin Receptors, and the Control of Body Weight, Nutrition Reviews, vol.56, issue.5475, p.3846, 1998.
DOI : 10.1111/j.1753-4887.1998.tb01685.x

J. M. Friedman, Obesity in the new millennium, Nature, issue.6778, p.404632634, 2000.

J. M. Friedman and J. L. Halaas, Leptin and the regulation of body weight in mammals, Nature, issue.6704, p.395763770, 1998.

A. D. Gaetano, T. Hardy, B. Beck, E. Abu-raddad, P. Palumbo et al., Mathematical models of diabetes progression, AJP: Endocrinology and Metabolism, vol.295, issue.6, pp.295-1462, 2008.
DOI : 10.1152/ajpendo.90444.2008

J. S. Garrow, Energy balance in manan overview. The American journal of clinical nutrition, p.11141119, 1987.

A. Goldbeter, A model for the dynamics of human weight cycling, Journal of Biosciences, vol.184, issue.1, p.129136, 2006.
DOI : 10.1007/BF02705242

P. L. Golden, T. J. Maccagnan, and W. M. Pardridge, Human blood-brain barrier leptin receptor. Binding and endocytosis in isolated human brain microvessels. The journal of clinical investigation, p.1418, 1997.

J. A. Greenberg and C. N. Boozer, Metabolic mass, metabolic rate, caloric restriction, and aging in male scher 344 rats, Mechanisms of ageing and development, vol.113, issue.1, p.3748, 2000.

J. Guo and K. D. Hall, Estimating the Continuous-Time Dynamics of Energy and Fat Metabolism in Mice, PLoS Computational Biology, vol.4, issue.9, p.1000511, 2009.
DOI : 10.1371/journal.pcbi.1000511.g003

J. Guo and K. D. Hall, Predicting Changes of Body Weight, Body Fat, Energy Expenditure and Metabolic Fuel Selection in C57BL/6 Mice, PLoS ONE, vol.298, issue.1, p.15961, 2011.
DOI : 10.1371/journal.pone.0015961.s003

S. J. Guyenet and M. W. Schwartz, Regulation of Food Intake, Energy Balance, and Body Fat Mass: Implications for the Pathogenesis and Treatment of Obesity, The Journal of Clinical Endocrinology & Metabolism, vol.97, issue.3, p.97745755, 2012.
DOI : 10.1210/jc.2011-2525

J. L. Halaas, C. Boozer, J. Blair-west, N. Fidahusein, D. A. Denton et al., Physiological response to long-term peripheral and central leptin infusion in lean and obese mice, Proceedings of the National Academy of Sciences, pp.948878-8883, 1997.
DOI : 10.1073/pnas.94.16.8878

J. L. Halaas and J. M. Friedman, Leptin and its receptor, Journal of Endocrinology, vol.155, issue.2, p.215216, 1997.
DOI : 10.1677/joe.0.1550215

K. D. Hall, Computational model of in vivo human energy metabolism during semistarvation and refeeding, AJP: Endocrinology and Metabolism, vol.291, issue.1, pp.23-37, 2006.
DOI : 10.1152/ajpendo.00523.2005

K. D. Hall, Body fat and fat-free mass inter-relationships: Forbes's theory revisited, British Journal of Nutrition, vol.97, issue.06, p.10591063, 2007.
DOI : 10.1017/S0007114507691946

K. D. Hall, What is the required energy decit per unit weight loss?, International Journal of Obesity, vol.32, issue.3, p.573576, 2008.

K. D. Hall, Mathematical modelling of energy expenditure during tissue deposition, British Journal of Nutrition, vol.77, issue.01, p.47, 2010.
DOI : 10.1038/oby.2007.364

K. D. Hall, Predicting metabolic adaptation, body weight change, and energy intake in humans, AJP: Endocrinology and Metabolism, vol.298, issue.3, pp.449-466, 2010.
DOI : 10.1152/ajpendo.00559.2009

K. D. Hall, Modeling Metabolic Adaptations and Energy Regulation in Humans, Annual Review of Nutrition, vol.32, issue.1, p.3554, 2012.
DOI : 10.1146/annurev-nutr-071811-150705

K. D. Hall, H. L. Bain, and C. C. Chow, How adaptations of substrate utilization regulate body composition, International Journal of Obesity, vol.19, issue.9, p.3113781383, 2007.
DOI : 10.1038/sj.ijo.0803608

K. D. Hall and V. E. Baracos, Computational modeling of cancer cachexia, Current Opinion in Clinical Nutrition and Metabolic Care, vol.11, issue.3, p.214221, 2008.
DOI : 10.1097/MCO.0b013e3282f9ae4d

K. D. Hall, N. F. Butte, B. A. Swinburn, and C. C. Chow, Dynamics of childhood growth and obesity: development and validation of a quantitative mathematical model, The Lancet Diabetes & Endocrinology, vol.1, issue.2, 2013.
DOI : 10.1016/S2213-8587(13)70051-2

K. D. Hall and P. N. Jordan, Modeling weight-loss maintenance to help prevent body weight regain. The American journal of clinical nutrition, p.14951503, 2008.

K. D. Hall, G. Sacks, D. Chandramohan, C. C. Chow, Y. C. Wang et al., Quantication of the eect of energy imbalance on bodyweight, Lancet, issue.9793, p.378826837, 2011.

S. C. Higgins, M. Gueorguiev, and M. Korbonits, Ghrelin, the peripheral hunger hormone, Annals of Medicine, vol.15, issue.2, p.116136, 2007.
DOI : 10.2337/diabetes.52.10.2546

G. W. Horgan, The behaviour of a neutral model of weight regulated only by body mass, Journal of Theoretical Biology, vol.270, issue.1, pp.16-177, 2011.
DOI : 10.1016/j.jtbi.2010.11.001
URL : https://hal.archives-ouvertes.fr/hal-00656336

S. Iossa, L. Lionetti, M. P. Mollica, A. Barletta, and G. Liverini, Energy intake and utilization vary during development in rats, The Journal of nutrition, issue.8, pp.1291593-1596, 1999.

M. Jacquier, F. Crauste, C. O. Soulage, and H. A. Soula, A Predictive Model of the Dynamics of Body Weight and Food Intake in Rats Submitted to Caloric Restrictions, PLoS ONE, vol.273, issue.6, p.100073, 2014.
DOI : 10.1371/journal.pone.0100073.t006
URL : https://hal.archives-ouvertes.fr/hal-01017357

M. Jacquier, H. A. Soula, C. , and F. , A mathematical model of leptin resistance, Mathematical Biosciences, vol.267, p.1023, 2015.
DOI : 10.1016/j.mbs.2015.06.008
URL : https://hal.archives-ouvertes.fr/hal-01233483

P. N. Jordan and K. D. Hall, Dynamic coordination of macronutrient balance during infant growth: insights from a mathematical model, The American journal of clinical nutrition, vol.87, issue.3, p.692703, 2008.

S. E. Kahn, R. L. Hull, and K. M. Utzschneider, Mechanisms linking obesity to insulin resistance and type 2 diabetes, Nature, vol.286, issue.7121, p.444840846, 2006.
DOI : 10.1038/nature05482

L. M. Kalm and R. D. Semba, They starved so that others be better fed: remembering ancel keys and the Minnesota experiment, The Journal of nutrition, vol.135, issue.6, pp.1347-1352, 2005.

M. L. Kaplan, J. R. Trout, and P. Smith, Adipocyte size distribution in fa/fa rats during development, Metabolism, vol.29, issue.4, p.333339, 1980.

R. E. Keesey and M. D. Hirvonen, The body-weight set point, Postgraduate Medicine, vol.36, issue.1, pp.1875-1883, 1997.
DOI : 10.1016/S0140-6736(69)90109-3

T. Kenakin, Principles: Receptor theory in pharmacology, Trends in Pharmacological Sciences, vol.25, issue.4, p.186192, 2004.
DOI : 10.1016/j.tips.2004.02.012

F. P. Kozusko, Body Weight Setpoint, Metabolic Adaption and Human Starvation, Bulletin of Mathematical Biology, vol.63, issue.2, p.393403, 2001.
DOI : 10.1006/bulm.2001.0229

R. L. Leibel, M. Rosenbaum, H. , and J. , Changes in Energy Expenditure Resulting from Altered Body Weight, New England Journal of Medicine, vol.332, issue.10, pp.332621-628, 1995.
DOI : 10.1056/NEJM199503093321001

E. H. Livingston and I. Kohlstadt, Simplied resting metabolic rate-predicting formulas for normal-sized and obese individuals, Obes Res, vol.13, issue.7, p.12551262, 2005.

B. B. Lowell and B. M. Spiegelman, Towards a molecular understanding of adaptive thermogenesis, Nature, issue.6778, p.404652660, 2000.

R. B. Lynn, G. Y. Cao, R. V. Considine, T. M. Hyde, C. et al., Autoradiographic localization of leptin binding in the choroid plexus of ob, Biochemical and Biophysical Research Communications, p.884889, 1996.

C. S. Mantzoros, The Role of Leptin in Human Obesity and Disease: A Review of Current Evidence, Annals of Internal Medicine, vol.130, issue.8, p.130671680, 1999.
DOI : 10.7326/0003-4819-130-8-199904200-00014

S. Margetic, C. Gazzola, G. G. Pegg, and R. A. Hill, Leptin: a review of its peripheral actions and interactions, International Journal of Obesity, vol.26, issue.11, p.2614071433, 2002.
DOI : 10.1038/sj.ijo.0802142

R. L. Martin, E. Perez, Y. J. He, R. Dawson, M. et al., Leptin resistance is associated with hypothalamic leptin receptor mRNA and protein downregulation, Metabolism, vol.49, issue.11, p.4914791484, 2000.
DOI : 10.1053/meta.2000.17695

R. J. Mccarter and J. Palmer, Energy metabolism and aging: a lifelong study of Fischer 344 rats, American Journal of Physiology -Endocrinology and Metabolism, vol.263, issue.3, pp.448-452, 1992.

G. J. Morton, T. H. Meek, and M. W. Schwartz, Neurobiology of food intake in health and disease, Nature Reviews Neuroscience, vol.29, issue.6, p.15367378, 2014.
DOI : 10.1126/science.299.5608.846

H. Münzberg, . Myers, and M. G. Jr, Molecular and anatomical determinants of central leptin resistance, Nature Neuroscience, vol.276, issue.5, p.566570, 2005.
DOI : 10.1159/000054353

M. G. Myers, M. A. Cowley, and H. Münzberg, Mechanisms of Leptin Action and Leptin Resistance, Annual Review of Physiology, vol.70, issue.1, p.537556, 2008.
DOI : 10.1146/annurev.physiol.70.113006.100707

M. G. Myers, R. L. Leibel, R. J. Seeley, and M. W. Schwartz, Obesity and leptin resistance: distinguishing cause from effect, Trends in Endocrinology & Metabolism, vol.21, issue.11, p.643651, 2010.
DOI : 10.1016/j.tem.2010.08.002

J. Naukkarinen, A. Rissanen, J. Kaprio, and K. H. Pietiläinen, Causes and consequences of obesity: the contribution of recent twin studies, International Journal of Obesity, vol.109, issue.8, p.3610171024, 2012.
DOI : 10.1002/(SICI)1097-0258(19980228)17:4<407::AID-SIM742>3.3.CO;2-C

J. A. Nelder and R. Mead, A Simplex Method for Function Minimization, The Computer Journal, vol.7, issue.4, p.308313, 1965.
DOI : 10.1093/comjnl/7.4.308

K. M. Nelson, R. L. Weinsier, C. L. Long, and Y. Schutz, Prediction of resting energy expenditure from fat-free mass and fat mass, The American journal of clinical nutrition, issue.5, p.56848856, 1992.

F. D. Newby, M. Digirolamo, G. A. Cotsonis, and M. H. Kutner, Model of spontaneous obesity in aging male wistar rats, American Journal of Physiology - Regulatory, Integrative and Comparative Physiology, issue.6 2, pp.259-1117, 1990.

R. Pal and A. Sahu, Leptin Signaling in the Hypothalamus during Chronic Central Leptin Infusion, Endocrinology, vol.144, issue.9, p.37893798, 2003.
DOI : 10.1210/en.2002-0148

F. Peelman, L. Zabeau, K. Moharana, S. N. Savvides, and J. Tavernier, 20 YEARS OF LEPTIN: Insights into signaling assemblies of the leptin receptor, Journal of Endocrinology, vol.223, issue.1, p.923, 2014.
DOI : 10.1530/JOE-14-0264

V. Periwal and C. C. Chow, Patterns in food intake correlate with body mass index, AJP: Endocrinology and Metabolism, vol.291, issue.5, pp.929-936, 2006.
DOI : 10.1152/ajpendo.00122.2006

R. A. Reimer, A. D. Maurer, D. C. Lau, and R. N. Auer, Long-term dietary restriction inuences plasma ghrelin and GOAT mRNA level in rats, Physiology & Behavior, issue.5, p.99605610, 2010.

E. D. Rosen and B. M. Spiegelman, Adipocytes as regulators of energy balance and glucose homeostasis, Nature, vol.112, issue.7121, p.444847853, 2006.
DOI : 10.1038/nature05483

M. Rosenbaum and R. L. Leibel, Adaptive thermogenesis in humans, International Journal of Obesity, vol.44, issue.1, pp.47-55, 2010.
DOI : 10.1056/NEJMoa040388

M. Rosenbaum and R. L. Leibel, 20 YEARS OF LEPTIN: Role of leptin in energy homeostasis in humans, Journal of Endocrinology, vol.223, issue.1, pp.83-96, 2014.
DOI : 10.1530/JOE-14-0358

L. Rossmeislová, L. Mali²ová, J. Kra£merová, and V. , Adaptation of human adipose tissue to hypocaloric diet, International Journal of Obesity, vol.2, issue.5, p.650, 2013.
DOI : 10.1038/sj.ijo.0803761

R. R. Ruolo, Review important concepts of receptor theory, Journal of Autonomic Pharmacology, vol.2, issue.4, p.277295, 1982.

A. Sahu, Resistance to the Satiety Action of Leptin Following Chronic Central Leptin Infusion is Associated with the Development of Leptin Resistance in Neuropeptide Y Neurones, Journal of Neuroendocrinology, vol.136, issue.10, p.14796804, 2002.
DOI : 10.1046/j.1365-2826.2002.00840.x

A. Sahu, R. E. Carraway, W. , and Y. P. , Evidence that neurotensin mediates the central eect of leptin on food intake in rat, Brain research, vol.888, issue.2, p.343347, 2001.

A. Sahu and S. P. Kalra, Neuropeptidergic regulation of feeding behavior, Trends in Endocrinology & Metabolism, vol.4, issue.7, p.217224, 1993.
DOI : 10.1016/1043-2760(93)90125-X

P. J. Scarpace, M. Matheny, R. L. Moore, and N. Tümer, Impaired leptin responsiveness in aged rats, Diabetes, vol.49, issue.3, p.49431435, 2000.
DOI : 10.2337/diabetes.49.3.431

P. J. Scarpace, M. Matheny, and N. Tümer, Hypothalamic leptin resistance is associated with impaired leptin signal transduction in aged obese rats, Neuroscience, vol.104, issue.4, p.11111117, 2001.
DOI : 10.1016/S0306-4522(01)00142-7

P. J. Scarpace, M. Matheny, N. Tümer, K. Y. Cheng, and Y. Zhang, Leptin resistance exacerbates diet-induced obesity and is associated with diminished maximal leptin signalling capacity in rats, Diabetologia, vol.144, issue.6, p.4810751083, 2005.
DOI : 10.1007/s00125-005-1763-x

P. J. Scarpace and N. Tümer, Peripheral and hypothalamic leptin resistance with age-related obesity, Physiology & Behavior, vol.74, issue.4-5, pp.4-5721727, 2001.
DOI : 10.1016/S0031-9384(01)00616-3

P. J. Scarpace and Y. Zhang, Leptin resistance: a prediposing factor for diet-induced obesity, AJP: Regulatory, Integrative and Comparative Physiology, vol.296, issue.3, pp.493-500, 2009.
DOI : 10.1152/ajpregu.90669.2008

R. Schemmel, O. Mickelsen, and J. L. Gill, Dietary obesity in rats: Body weight and body fat accretion in seven strains of rats, The Journal of nutrition, vol.100, issue.9, pp.1041-1048, 1970.

M. W. Schwartz, E. Peskind, M. Raskind, E. J. Boyko, and D. Porte, Cerebrospinal uid leptin levels: relationship to plasma levels and to adiposity in humans, Nature medicine, vol.2, issue.5, pp.589593-181, 1996.

M. W. Schwartz, S. C. Woods, D. Porte, R. J. Seeley, and D. G. Baskin, Central nervous system control of food intake, Nature, issue.6778, p.404661671, 2000.

A. Shapiro, N. Tümer, Y. Gao, K. Cheng, and P. J. Scarpace, Prevention and reversal of diet-induced leptin resistance with a sugar-free diet despite high fat content, British Journal of Nutrition, vol.79, issue.03, p.390397, 2011.
DOI : 10.1073/pnas.0709778104

E. W. Shek, M. W. Brands, and J. E. Hall, Chronic Leptin Infusion Increases Arterial Pressure, Hypertension, vol.31, issue.1, p.31409414, 1998.
DOI : 10.1161/01.HYP.31.1.409

B. Song and D. M. Thomas, Dynamics of starvation in humans, Journal of Mathematical Biology, vol.71, issue.5, p.2743, 2007.
DOI : 10.1007/s00285-006-0037-7

H. A. Soula, A. Géloën, and C. O. Soulage, Model of adipose tissue cellularity dynamics during food restriction, Journal of Theoretical Biology, vol.364, p.189196, 2015.
DOI : 10.1016/j.jtbi.2014.08.046
URL : https://hal.archives-ouvertes.fr/hal-01092535

H. A. Soula, H. Julienne, C. O. Soulage, and A. Géloën, Modelling adipocytes size distribution, Journal of Theoretical Biology, vol.332, p.8995, 2013.
DOI : 10.1016/j.jtbi.2013.04.025
URL : https://hal.archives-ouvertes.fr/hal-00850474

C. Soulage, B. Zarrouki, A. F. Soares, M. Lagarde, and A. Geloen, Lou/c obesity-resistant rat exhibits hyperactivity, hypermetabolism, alterations in white adipose tissue cellularity, and lipid tissue proles, Endocrinology, issue.2, p.149615625, 2008.

T. W. Stephens, M. Basinski, P. K. Bristow, J. M. Bue-valleskey, S. G. Burgett et al., The role of neuropeptide Y in the antiobesity action of the obese gene product, Nature, vol.377, issue.6549, p.377530532, 1995.
DOI : 10.1038/377530a0

R. P. Stephenson, A modication of receptor theory, British journal of pharmacology and chemotherapy, vol.11, issue.4, p.379393, 1956.

J. Tam, D. Fukumura, and R. K. Jain, A Mathematical Model of Murine Metabolic Regulation by Leptin: Energy Balance and Defense of a Stable Body Weight, Cell Metabolism, vol.9, issue.1, p.5263, 2009.
DOI : 10.1016/j.cmet.2008.11.005

L. A. Tartaglia, The Leptin Receptor, Journal of Biological Chemistry, vol.272, issue.10, p.60936096, 1997.
DOI : 10.1074/jbc.272.10.6093

L. A. Tartaglia, M. Dembski, X. Weng, N. Deng, J. Culpepper et al., Identication and expression cloning of a leptin receptor, Cell, issue.7, p.8312631271, 1995.

D. Thomas, S. K. Das, J. A. Levine, C. K. Martin, L. Mayer et al., New fat free mass - fat mass model for use in physiological energy balance equations, Nutrition & Metabolism, vol.7, issue.1, p.39, 2010.
DOI : 10.1126/science.1106561

D. M. Thomas, A. Ciesla, J. A. Levine, J. G. Stevens, M. et al., A mathematical model of weight change with adaptation, Mathematical Biosciences and Engineering, vol.6, issue.4, p.873887, 2009.
DOI : 10.3934/mbe.2009.6.873

D. M. Thomas, M. C. Gonzalez, A. Z. Pereira, L. M. Redman, and S. B. Heymseld, Time to Correctly Predict the Amount of Weight Loss with Dieting, Journal of the Academy of Nutrition and Dietetics, vol.114, issue.6, p.857861, 2014.
DOI : 10.1016/j.jand.2014.02.003

D. M. Thomas, C. K. Martin, S. Heymseld, L. M. Redman, D. A. Schoeller et al., A simple model predicting individual weight change in humans, Journal of Biological Dynamics, vol.136, issue.6, p.579599, 2011.
DOI : 10.1186/1743-7075-1-5

D. M. Thomas, J. E. Navarro-barrientos, D. E. Rivera, S. B. Heymseld, C. Bredlau et al., Dynamic energy-balance model predicting gestational weight gain. The American journal of clinical nutrition, p.115122, 2012.

D. M. Thomas, D. A. Schoeller, L. A. Redman, C. K. Martin, J. A. Levine et al., A computational model to determine energy intake during weight loss. The American journal of clinical nutrition, p.9213261331, 2010.

B. Topp, K. Promislow, G. Devries, R. M. Miura, and D. T. Finegood, A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes, Journal of Theoretical Biology, vol.206, issue.4, p.605619, 2000.

A. Tremblay, M. Royer, J. Chaput, and E. Doucet, Adaptive thermogenesis can make a dierence in the ability of obese individuals to lose body weight, International Journal of Obesity, vol.37, issue.6, p.759764, 2013.

M. Tschöp, D. L. Smiley, and M. L. Heiman, Ghrelin induces adiposity in rodents, Nature, issue.6806, p.407908913, 2000.

I. M. Van-leeuwen, F. D. Kelpin, and S. A. Kooijman, A mathematical model that accounts for the eects of caloric restriction on body weight and longevity, Biogerontology, vol.3, issue.6, p.373381, 2002.

E. T. Vestergaard, T. K. Hansen, L. C. Gormsen, P. Jakobsen, N. Moller et al., Constant intravenous ghrelin infusion in healthy young men: clinical pharmacokinetics and metabolic effects, AJP: Endocrinology and Metabolism, vol.292, issue.6, pp.1829-1836, 2007.
DOI : 10.1152/ajpendo.00682.2006

N. D. Volkow, G. Wang, and R. D. Baler, Reward, dopamine and the control of food intake: implications for obesity, Trends in Cognitive Sciences, vol.15, issue.1, p.3746, 2011.
DOI : 10.1016/j.tics.2010.11.001

J. Wang, S. Obici, K. Morgan, N. Barzilai, Z. Feng et al., Overfeeding Rapidly Induces Leptin and Insulin Resistance, Diabetes, vol.50, issue.12, p.5027862791, 2001.
DOI : 10.2337/diabetes.50.12.2786

M. Y. Wang, Y. Lee, and R. H. Unger, Novel Form of Lipolysis Induced by Leptin, Journal of Biological Chemistry, vol.274, issue.25, p.2741754117544, 1999.
DOI : 10.1074/jbc.274.25.17541

P. S. Widdowson, R. Upton, R. Buckingham, J. Arch, W. et al., Inhibition of Food Response to Intracerebroventricular Injection of Leptin Is Attenuated in Rats With Diet-Induced Obesity, Diabetes, vol.46, issue.11, p.4617821785, 1997.
DOI : 10.2337/diab.46.11.1782

S. L. Wijers, W. H. Saris, and W. D. Van-marken-lichtenbelt, Recent advances in adaptive thermogenesis: potential implications for the treatment of obesity, Obesity Reviews, vol.20, issue.2, p.218226, 2009.
DOI : 10.1111/j.1467-789X.2008.00538.x

J. Wilsey and P. J. Scarpace, Caloric restriction reverses the decits in leptin receptor protein and leptin signaling capacity associated with diet-induced obesity: role of leptin in the regulation of hypothalamic long-form leptin receptor expression, Journal of endocrinology, vol.181, issue.2, p.297306, 2004.

D. Wirtshafter and J. D. Davis, Set points, settling points, and the control of body weight???, Physiology & Behavior, vol.19, issue.1, p.7578, 1977.
DOI : 10.1016/0031-9384(77)90162-7

S. C. Woods, M. W. Schwartz, D. G. Baskin, and R. J. Seeley, Food Intake and the Regulation of Body Weight, Annual Review of Psychology, vol.51, issue.1, p.255277, 2000.
DOI : 10.1146/annurev.psych.51.1.255

S. C. Woods, R. J. Seeley, D. Porte, and M. W. Schwartz, Signals That Regulate Food Intake and Energy Homeostasis, Science, vol.280, issue.5368, p.28013781383, 1998.
DOI : 10.1126/science.280.5368.1378

A. M. Wren, L. J. Seal, M. A. Cohen, A. E. Brynes, G. S. Frost et al., Ghrelin Enhances Appetite and Increases Food Intake in Humans, The Journal of Clinical Endocrinology & Metabolism, vol.86, issue.12, p.865992, 2001.
DOI : 10.1210/jcem.86.12.8111

J. Zeng, B. W. Patterson, S. Klein, D. R. Martin, S. Dagogo-jack et al., Whole body leptin kinetics and renal metabolism in vivo, American Journal of Physiology -Endocrinology and Metabolism, issue.6, pp.273-1102, 1997.

Y. Zhang, M. Olbort, K. Schwarzer, B. Nuesslein-hildesheim, M. Nicolson et al., The Leptin Receptor Mediates Apparent Autocrine Regulation of Leptin Gene Expression, Biochemical and Biophysical Research Communications, p.492495, 1997.
DOI : 10.1006/bbrc.1997.7622

Y. Zhang, R. Proenca, M. Maei, M. Barone, L. Leopold et al., Positional cloning of the mouse obese gene and its human homologue, Nature, vol.372, issue.6505, p.372425432, 1994.
DOI : 10.1038/372425a0

Y. Zhang and P. J. Scarpace, The role of leptin in leptin resistance and obesity, Physiology & Behavior, vol.88, issue.3, 2006.
DOI : 10.1016/j.physbeh.2006.05.038