L. Abbott, V. Vreeswijk, and C. , Asynchronous states in networks of pulse-coupled neuron, Phys Rev, vol.48, pp.1483-1490, 1993.

S. Amari, Characteristics of random nets of analog neuron-like elements, 1972.

S. Amari, K. Yoshida, and K. Kanatani, A Mathematical Foundation for Statistical Neurodynamics, SIAM Journal on Applied Mathematics, vol.33, issue.1, pp.95-126, 1977.
DOI : 10.1137/0133008

G. Ben-arous and A. Guionnet, Large deviations for Langevin spin glass dynamics, Probability Theory and Related Fields, vol.47, issue.32, pp.455-509, 1995.
DOI : 10.1007/BF01198846

G. Ben-arous and A. Guionnet, Symmetric Langevin spin glass dynamics, The Annals of Probability, vol.25, issue.3, pp.1367-1422, 1997.
DOI : 10.1214/aop/1024404517

V. Bogachev, Gaussian Measures, Cortex: Statistics and Geometry of Neuronal Connectivity, 1998.
DOI : 10.1090/surv/062

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

B. Cessac, Increase in Complexity in Random Neural Networks, Journal de Physique I, vol.5, issue.3, pp.409-432, 1995.
DOI : 10.1051/jp1:1995135
URL : https://hal.archives-ouvertes.fr/jpa-00247065

A. Crisanti and H. Sompolinsky, Dynamics of spin systems with randomly asymmetric bonds: Langevin dynamics and a spherical model, Physical Review A, vol.36, issue.10, pp.4922-4939, 1987.
DOI : 10.1103/PhysRevA.36.4922

A. Crisanti and H. Sompolinsky, Dynamics of spin systems with randomly asymmetric bonds: Ising spins and Glauber dynamics, Physical Review A, vol.37, issue.12, p.4865, 1987.
DOI : 10.1103/PhysRevA.37.4865

P. Dayan and L. Abbott, Theoretical Neuroscience : Computational and Mathematical Modeling of Neural Systems, 2001.

B. Ermentrout, Neural networks as spatio-temporal pattern-forming systems, Reports on Progress in Physics, vol.61, issue.4, pp.353-430, 1998.
DOI : 10.1088/0034-4885/61/4/002
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.6053

W. Freeman, Mass action in the nervous system, 1975.

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 and W. Kistler, Mathematical formulations of Hebbian learning, Biological Cybernetics, vol.87, issue.5-6, pp.404-415, 2002.
DOI : 10.1007/s00422-002-0353-y

F. Grimbert and O. Faugeras, Bifurcation Analysis of Jansen's Neural Mass Model, Neural Computation, vol.18, issue.12, pp.3052-3068, 2006.
DOI : 10.1007/s004220000160

A. Guionnet, Averaged and quenched propagation of chaos for spin glass dynamics. Probability Theory and Related Fields, pp.183-215, 1997.

J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons., Proceedings of the National Academy of Sciences, pp.3088-3092, 1984.
DOI : 10.1073/pnas.81.10.3088

A. Houghton, S. Jain, and A. Young, Role of initial conditions in the mean-field theory of spin-glass dynamics, Physical Review B, vol.28, issue.5, pp.2630-2637, 1983.
DOI : 10.1103/PhysRevB.28.2630

B. Jansen and V. Rit, Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns, Biological Cybernetics, vol.580, issue.4, pp.357-366, 1995.
DOI : 10.1007/BF00199471

I. Karatzas and S. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol.113, 1991.
DOI : 10.1007/978-1-4612-0949-2

M. Mattia, D. Giudice, and P. , Population dynamics of interacting spiking neurons, Physical Review E, vol.66, issue.5, p.51917, 2002.
DOI : 10.1103/PhysRevE.66.051917

L. Molgedey, J. Schuchardt, and H. Schuster, Suppressing chaos in neural networks by noise, Physical Review Letters, vol.69, issue.26, pp.3717-3719, 1992.
DOI : 10.1103/PhysRevLett.69.3717

O. Moynot and M. Samuelides, Large deviations and mean-field theory for asymmetric random recurrent neural networks, Probability Theory and Related Fields, vol.123, issue.1, pp.41-75, 2002.
DOI : 10.1007/s004400100182

A. Van-rotterdam, F. Lopes-da-silva, J. Van-den-ende, M. Viergever, and A. Hermans, A model of the spatial-temporal characteristics of the alpha rhythm, Bulletin of Mathematical Biology, vol.31, issue.No. 1, p.283, 1982.
DOI : 10.1007/BF02463252

M. Samuelides and B. Cessac, Random recurrent neural networks, European Physical Journal - Special Topics, vol.142, pp.7-88, 2007.
DOI : 10.1140/epjst/e2007-00059-1
URL : https://hal.archives-ouvertes.fr/inria-00529560

H. Sompolinsky and A. Zippelius, Relaxational dynamics of the Edwards-Anderson model and the mean-field theory of spin-glasses, Physical Review B, vol.25, issue.11, pp.6860-6875, 1982.
DOI : 10.1103/PhysRevB.25.6860

H. Sompolinsky, A. Crisanti, and H. Sommers, Chaos in Random Neural Networks, Random Neural Networks, pp.259-262, 1988.
DOI : 10.1103/PhysRevLett.61.259

A. Treves, Mean-field analysis of neuronal spike dynamics, Network: Computation in Neural Systems, vol.4, issue.3, pp.259-284, 1993.
DOI : 10.1088/0954-898X_4_3_002

. Unité-de-recherche-inria-sophia and . Antipolis, route des Lucioles -BP 93 -06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université -ZAC des Vignes 4, 2004.

I. Unité-de-recherche and . Lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt, Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex

I. De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399