L. , A. , and C. Van-vreeswijk, Asynchronous states in networks of pulse-coupled oscillators, Phys. Rev. E, vol.48, pp.1483-1490, 1993.

L. Abbott, Lapicque???s introduction of the integrate-and-fire model neuron (1907), Brain Research Bulletin, vol.50, issue.5-6, pp.303-304, 1907.
DOI : 10.1016/S0361-9230(99)00161-6

P. C. Bressloff and J. M. Newby, Stochastic models of intra-cellular transport, Review of Modern Physics, vol.85, issue.1, p.2013

N. Brunel and M. Van-rossum, Lapicque???s 1907 paper: from frogs to integrate-and-fire, Biological Cybernetics, vol.5, issue.2, pp.341-349, 2007.
DOI : 10.1007/s00422-007-0190-0

N. Brunel, Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons, Journal of Computational Neuroscience, vol.8, issue.3, pp.183-208, 2000.
DOI : 10.1023/A:1008925309027

N. Brunel and V. Hakim, Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates, Neural Computation, vol.15, issue.7, pp.1621-1671, 1999.
DOI : 10.1038/373612a0

N. Brunel, C. Mark, and . Van-rossum, Quantitative investigations of electrical nerve excitation treated as polarization, Biological Cybernetics, vol.35, issue.35, pp.341-350, 2007.
DOI : 10.1007/s00422-007-0189-6

A. N. Burkitt, A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input, Biological Cybernetics, vol.68, issue.1, pp.1-19, 2006.
DOI : 10.1007/s00422-006-0068-6

J. María, . Cáceres, A. José, B. Carrillo, and . Perthame, Analysis of nonlinear noisy 470 integrate & fire neuron models: blow-up and steady states, The Journal of Mathematical Neuroscience, vol.1, 2011.

M. Deger, T. Schwalger, R. Naud, and W. Gerstner, Fluctuations and information filtering in coupled populations of spiking neurons with adaptation, Physical Review E, vol.90, issue.6, p.90062704, 2014.
DOI : 10.1103/PhysRevE.90.062704

G. Dumont and J. Henry, Population density models of integrate-and-fire neurons with jumps: well-posedness, Journal of Mathematical Biology, vol.17, issue.4, 2012.
DOI : 10.1007/s00285-012-0554-5

URL : https://hal.archives-ouvertes.fr/hal-00711492

G. Dumont, J. Henry, ]. G. Dumont, J. Henry, and C. O. Tarniceriu, Synchronization of an Excitatory Integrate-and-Fire Neural Network, Bulletin of Mathematical Biology, vol.17, issue.2, pp.629-677, 2013.
DOI : 10.1007/s11538-013-9823-8

URL : https://hal.archives-ouvertes.fr/hal-00822472

G. Dumont, C. Henry, A. Tarniceriu, . Faisal, D. Lp-selen et al., Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model Noise in the nervous system, Journal of Mathematical Biology Nature Reviews Neuroscience, vol.16, issue.94, pp.485292-303, 2008.

C. W. Gardiner, Handbook of Stochastic Method for Physics, Chemistry and Natural Sciences, 1996.

G. Gerstein and B. Mandelbrot, Random Walk Models for the Spike Activity of a Single Neuron, Biophysical Journal, vol.4, issue.1, pp.41-68, 1964.
DOI : 10.1016/S0006-3495(64)86768-0

W. Gerstner, Time structure of the activity in neural network models, Physical Review E, vol.51, issue.1, pp.738-758, 1995.
DOI : 10.1103/PhysRevE.51.738

W. Gerstner, W. Kistler, W. Gerstner, and R. Naud, Spiking neuron models How good are neuron models? Science, pp.495379-380, 2002.
DOI : 10.1017/cbo9780511815706

E. M. Izhikevich, Dynamical Systems in Neuroscience, 2007.

B. Knight, B. Knight, L. Manin, and . Sirovich, Dynamics of Encoding in Neuron Populations: Some General Mathematical Features, Dynamical models of interacting neuron populations in visual cortex. Robotics and cybernetics, pp.473-518, 1996.
DOI : 10.1007/BF00335237

B. Knight, Dynamics of Encoding in a Population of Neurons, The Journal of General Physiology, vol.59, issue.6, pp.734-766, 1972.
DOI : 10.1085/jgp.59.6.734

A. Longtin, Detecting and estimating signals in noisy cable sstructure. i: Neuronal noise sources, Neural Computation, vol.8, issue.11, pp.1618-5051797, 1999.

D. Millman, S. Mihalas, A. Kirkwood, E. Niebur, K. A. Newhall et al., Self-organized criticality occurs in non-conservative neuronal networks during 'up' states Dynamics of current-based, poisson driven, integrate-and-fire neuronal networks, Nature physics Communications in Mathematical Sciences, vol.6, issue.8, pp.801-805, 2010.

K. A. Newhall, G. Kovacic, P. R. Kramer, and D. Cai, Cascadeinduced synchrony in stochastically-driven neuronal networks, p.515, 2010.
DOI : 10.1103/physreve.82.041903

Q. Duane, D. Nykamp, and . Tranchina, A population density appraoch that facilitates large-scale modeling of neural networks : analysis and an application to orientation tuning, Journal of computational neurosciences, vol.8, pp.19-50, 2000.

A. Omurtag, L. Knight, S. Sirovich, . Ostojic, V. Brunel et al., On the simulation of large population of neurons Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities, Journal of computational Journal of computational neurosciences, vol.833, issue.26, pp.51-63, 2000.

K. Pakdaman, D. Perthame, and . Salort, Dynamics of a structured neuron population Khashayar Pakdaman, Beno??tBeno??t Perthame, and Delphine Salort. Relaxation and selfsustained oscillations in the time elapsed neuron network model, Nonlinearity SIAM Journal of Applied Mathematics, vol.2335, issue.3, pp.23-55, 2009.

H. E. Plesser and W. Gerstner, Noise in Integrate-and-Fire Neurons: From Stochastic Input to Escape Rates, Neural Computation, vol.18, issue.2, pp.367-384, 2000.
DOI : 10.1016/S0006-3495(72)86068-5

M. Shadlen and W. Newsome, Noise, neural codes and cortical organization, Current Opinion in Neurobiology, vol.4, issue.4
DOI : 10.1016/0959-4388(94)90059-0

W. Softky and C. Koch, The highly irregular firing of cortical cells is inconsistent with temporal integration of random epsps, Journal of Neuroscience, vol.13, pp.334-380, 1993.

R. Stein, Some Models of Neuronal Variability, 40] H. von Foerster. Some remarks on changing populations, pp.37-68, 1959.
DOI : 10.1016/S0006-3495(67)86574-3

J. A. White, J. T. Rubinstein, and A. R. Kay, Channel noise in neurons, Trends in Neurosciences, vol.23, issue.3, pp.131-137, 2000.
DOI : 10.1016/S0166-2236(99)01521-0

W. J. Wilbur and J. , A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions, Journal of Theoretical Biology, vol.105, issue.2, pp.345-368, 1983.
DOI : 10.1016/S0022-5193(83)80013-7