Characteristics of random nets of analog neuron-like elements, Systems, Man and Cybernetics, vol.2, issue.5, pp.643-657, 1972. ,
Dynamics of pattern formation in lateral-inhibition type neural fields, Biological Cybernetics, vol.13, issue.2, pp.77-87, 1977. ,
DOI : 10.1007/BF00337259
A Mathematical Foundation for Statistical Neurodynamics, SIAM Journal on Applied Mathematics, vol.33, issue.1, pp.95-126, 1977. ,
DOI : 10.1137/0133008
Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex, Cerebral Cortex, vol.7, issue.3, pp.237-252, 1997. ,
DOI : 10.1093/cercor/7.3.237
Random Dynamical Systems, p.157, 1998. ,
Large deviations for langevin spin glass dynamics. Probability Theory and Related Fields, pp.455-509, 1995. ,
DOI : 10.1007/bf01195482
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.7465
Symmetric langevin spin glass dynamics. The Annals of Probability, pp.1367-1422, 1997. ,
Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain, The Journal of Comparative Neurology, issue.5, pp.513532-541, 2009. ,
Mean field description of and propagation of chaos in recurrent multipopulation networks of hodgkin-huxley and fitzhugh-nagumo neurons Arxiv preprint, p.133, 2011. ,
Avalanches in a Stochastic Model of Spiking Neurons, PLoS Computational Biology, vol.26, issue.7, p.34, 2010. ,
DOI : 10.1371/journal.pcbi.1000846.s002
IntroductionàIntroductionà l'´ etude de la médecine expérimentale. ? Aditions Garnier-Flammarion, p.15, 1966. ,
DOI : 10.1522/cla.bec.int
URL : https://babel.hathitrust.org/cgi/imgsrv/download/pdf?id=uc1.b5585311;orient=0;size=100;seq=367;attachment=0
Enhanced EEG functional connectivity in mesial temporal lobe epilepsy, Epilepsy Research, vol.81, issue.1, pp.58-68, 2008. ,
DOI : 10.1016/j.eplepsyres.2008.04.020
URL : https://hal.archives-ouvertes.fr/inserm-00291171
Stochastic Neural Field Theory and the System-Size Expansion, SIAM Journal on Applied Mathematics, vol.70, issue.5, pp.1488-1521, 2009. ,
DOI : 10.1137/090756971
Metastable states and quasicycles in a stochastic wilson?cowan model, Physical Review E, vol.82, p.34, 2010. ,
What Geometric Visual Hallucinations Tell Us about the Visual Cortex, Neural Computation, vol.222, issue.8, pp.473-491, 2002. ,
DOI : 10.1007/BF00288786
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.146.572
Kronecker products and matrix calculus in system theory, IEEE Transactions on Circuits and Systems, p.60, 1978. ,
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
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
Field-theoretic approach to fluctuation effects in neural networks, Physical Review E, vol.75, issue.5, pp.75-109, 2007. ,
DOI : 10.1103/PhysRevE.75.051919
Statistical mechanics of the neocortex, Progress in Biophysics and Molecular Biology, vol.99, issue.2-3, pp.53-86, 2009. ,
DOI : 10.1016/j.pbiomolbio.2009.07.003
Systematic Fluctuation Expansion for Neural Network Activity Equations, Neural Computation, vol.13, issue.1, pp.377-426, 2005. ,
DOI : 10.1093/acprof:oso/9780198509233.001.0001
Analysis of Nonlinear Noisy Integrate&Fire Neuron Models: blow-up and steady states, The Journal of Mathematical Neuroscience, vol.1, issue.1, p.134, 2011. ,
DOI : 10.1007/s11118-008-9093-5
Probabilistic approach for granular media equations in the non-uniformly convex case. Probability Theory and Related Fields, pp.19-40, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00021591
Mean-field equations, bifurcation map and route to chaos in discrete time neural networks, Physica D: Nonlinear Phenomena, vol.74, issue.1-2, pp.24-44, 1994. ,
DOI : 10.1016/0167-2789(94)90024-8
Bumps, Breathers, and Waves in a Neural Network with Spike Frequency Adaptation, Physical Review Letters, vol.94, issue.14, pp.94-127, 2005. ,
DOI : 10.1103/PhysRevLett.94.148102
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
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, pp.14-46, 2001. ,
Stochastic dynamics as a principle of brain function, Progress in Neurobiology, vol.88, issue.1, pp.1-16, 2009. ,
DOI : 10.1016/j.pneurobio.2009.01.006
Self-sustained asynchronous irregular states and Up???Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons, Journal of Computational Neuroscience, vol.74, issue.11, pp.493-506, 2008. ,
DOI : 10.1007/s10827-009-0164-4
URL : https://hal.archives-ouvertes.fr/hal-00444902
Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo, Journal of Neurophysiology, vol.81, issue.16, pp.1531-1547, 1999. ,
Numerical Continuation of Fold Bifurcations of Limit Cycles in MATCONT, Proceedings of the ICCS, pp.701-710, 2003. ,
DOI : 10.1007/3-540-44860-8_72
MATCONT, ACM Transactions on Mathematical Software, vol.29, issue.2, pp.141-164, 2003. ,
DOI : 10.1145/779359.779362
Prescribing a system of random variables by conditional distributions. Theory of Probability and its Applications, pp.15-45, 1970. ,
Decorrelated Neuronal Firing in Cortical Microcircuits, Science, vol.327, issue.5965, pp.584-587, 2010. ,
DOI : 10.1126/science.1179867
BRAIN DYNAMICS AT MULTIPLE SCALES: CAN ONE RECONCILE THE APPARENT LOW-DIMENSIONAL CHAOS OF MACROSCOPIC VARIABLES WITH THE SEEMINGLY STOCHASTIC BEHAVIOR OF SINGLE NEURONS?, International Journal of Bifurcation and Chaos, vol.20, issue.06, 2009. ,
DOI : 10.1142/S0218127410026769
URL : https://hal.archives-ouvertes.fr/hal-01179754
A Master Equation Formalism for Macroscopic Modeling of Asynchronous Irregular Activity States, Neural Computation, vol.85, issue.1, pp.46-100, 2009. ,
DOI : 10.1523/JNEUROSCI.3508-05.2005
URL : https://hal.archives-ouvertes.fr/hal-00377136
Temporal Binding, Binocular Rivalry, and Consciousness, Consciousness and Cognition, vol.8, issue.2, pp.128-151, 1999. ,
DOI : 10.1006/ccog.1999.0389
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.207.8191
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
Simulating, analyzing, and animating dynamical systems: A guide to xppaut for researchers and students, Society for Industrial Mathematics, p.63, 2002. ,
DOI : 10.1137/1.9780898718195
A mathematical theory of visual hallucination patterns, Biological Cybernetics, vol.135, issue.Suppl. 247, pp.137-150, 1979. ,
DOI : 10.1007/BF00336965
Mathematical Foundations of Neuroscience, Neuroscience, vol.15, issue.19 7, pp.31428-434, 2010. ,
Noise in the nervous system, Nature Reviews Neuroscience, vol.81, issue.4, pp.292-303, 2008. ,
DOI : 10.1126/science.1089662
Spontaneous subthreshold activity at motor nerve endings, Journal of Physiology, vol.117, issue.18, pp.109-128, 1952. ,
A constructive mean-field analysis of multi population neural networks with random synaptic weights and stochastic inputs, Frontiers in Computational Neuroscience, vol.3, issue.77, p.80, 2009. ,
DOI : 10.3389/neuro.10.001.2009
URL : https://hal.archives-ouvertes.fr/inria-00258345
Synaptic efficacy and the transmission of complex firing patterns between neurons, Journal of Neurophysiology, vol.84, pp.3010-3025, 2000. ,
Dynamics of the Firing Probability of Noisy Integrate-and-Fire Neurons, Neural Computation, vol.19, issue.9, pp.2057-2110, 2002. ,
DOI : 10.1111/j.1469-7793.1998.715bv.x
Correlation-Induced Synchronization of Oscillations in Olfactory Bulb Neurons, Journal of Neuroscience, vol.26, issue.14, pp.3646-3655, 2006. ,
DOI : 10.1523/JNEUROSCI.4605-05.2006
Spiking Neuron Models, p.46, 2002. ,
DOI : 10.1017/cbo9780511815706
Global attractor and asymptotic dynamics in the kuramoto model for coupled noisy phase oscillators Arxiv preprint, p.35, 2011. ,
Astrocytes Control Breathing Through pH-Dependent Release of ATP, Science, vol.329, issue.5991, pp.329571-575, 2010. ,
DOI : 10.1126/science.1190721
Averaged and quenched propagation of chaos for spin glass dynamics. Probability Theory and Related Fields, pp.183-215, 1997. ,
Non uniqueness of stationary measures for self-stabilizing diffusions, Stochastic Processes and their Applications, pp.1210-1246, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00368177
Receptive fields, binocular interaction and functional architecture in the cat's visual cortex, The Journal of Physiology, vol.160, issue.1, pp.106-154, 1962. ,
DOI : 10.1113/jphysiol.1962.sp006837
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
Brownian Motion and Stochastic Calculus, p.163, 1998. ,
DOI : 10.1007/978-1-4612-0949-2
Generalization in a linear perceptron in the presence of noise, Journal of Physics A: Mathematical and General, vol.25, issue.5, pp.1135-1147, 1992. ,
DOI : 10.1088/0305-4470/25/5/020
Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities, Journal of Statistical Physics, vol.39, issue.Suppl., pp.569-605, 1987. ,
DOI : 10.1007/BF01009349
Effects of noise in excitable systems, Physics Reports, vol.392, issue.6, pp.321-424, 2004. ,
DOI : 10.1016/j.physrep.2003.10.015
The neuronal basis for consciousness, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.353, issue.1377, pp.1841-1849, 1998. ,
DOI : 10.1098/rstb.1998.0336
Time-interval sequences in bistable systems and the noise-induced transmission of information by sensory neurons, Physical Review Letters, vol.67, issue.5, pp.656-659, 1991. ,
DOI : 10.1103/PhysRevLett.67.656
Critical Analysis of Dimension Reduction by a Moment Closure Method in a Population Density Approach to Neural Network Modeling, Neural Computation, vol.20, issue.8, pp.2032-2092, 2007. ,
DOI : 10.1016/S0006-3495(72)86068-5
Reliability of spike timing in neocortical neurons, Science, vol.268, issue.5216, pp.1503-1506, 1995. ,
DOI : 10.1126/science.7770778
Stochastic Differential Equations and Applications . Horwood publishing, pp.163-165, 2008. ,
On the poisson distribution derived from independent random walks, Natural Science Report Ochanomizu University, vol.6, issue.1, pp.1-6, 1955. ,
A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS, Proceedings of the National Academy of Sciences of the USA, pp.1907-1911, 1966. ,
DOI : 10.1073/pnas.56.6.1907
A new approach to quantitative chaos propagation estimates for drift, diffusion and jump processes, Arxiv Preprint, 2011. ,
Some Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix Products, Journal of the American Statistical Association, vol.40, issue.327, pp.953-963, 1969. ,
DOI : 10.1080/01621459.1969.10500970
Master-equation approach to stochastic neurodynamics, Physical Review E, vol.48, issue.3, pp.2259-2266, 1993. ,
DOI : 10.1103/PhysRevE.48.2259
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.8917
Coherence resonance and discharge time reliability in neurons and neuronal models, Neural Networks, vol.14, issue.6-7, pp.895-905, 2001. ,
DOI : 10.1016/S0893-6080(01)00025-9
The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics, p.16, 1989. ,
Neurogéométrie de la vision. Les Editions de l'Ecole Polytechnique, p.7, 2008. ,
Noiseinduced coherent oscilations in randomly connected neural networks, Physical Review E, vol.58, issue.129, pp.3610-3622, 1998. ,
The Noisy Brain: Stochastic Dynamics as a Principle of Brain Function, p.34, 2010. ,
Phase Synchronization of Chaotic Oscillators, Physical Review Letters, vol.76, issue.11, pp.1804-1807, 1996. ,
DOI : 10.1103/PhysRevLett.76.1804
Visual Feature Integration and the Temporal Correlation Hypothesis, Annual Review of Neuroscience, vol.18, issue.1, pp.555-586, 1995. ,
DOI : 10.1146/annurev.ne.18.030195.003011
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.6735
The highly irregular firing of cortical cells is inconsistent with temporal integration of random epsps, Journal of Neuroscience, vol.13, pp.334-350, 1993. ,
Chaos in Random Neural Networks, Physical Review Letters, vol.61, issue.3, pp.259-262, 1988. ,
DOI : 10.1103/PhysRevLett.61.259
Dale's principle and glutamate corelease from ventral midbrain dopamine neurons, Amino Acids, vol.19, issue.1, pp.45-52, 2000. ,
DOI : 10.1007/s007260070032
Equations de type de boltzmann, spatialement homogènes. Probability Theory and Related Fields, pp.559-592, 1984. ,
DOI : 10.1007/bf00531891
Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated, Journal of Functional Analysis, vol.56, issue.3, pp.311-336, 1984. ,
DOI : 10.1016/0022-1236(84)90080-6
A propagation of chaos result for burgers' equation. Probability Theory and Related Fields, pp.581-613, 1986. ,
Topics in propagation of chaos. Ecole d'Eté de Probabilités de Saint-Flour XIX, pp.165-190, 1989. ,
Probabilistic treatment of the boltzmann equation of maxwellian molecules. Probability Theory and Related Fields Some probabilistic problems in the spatially homogeneous boltzmann equation. Theory and Application of Random Fields, pp.67-105, 1978. ,
Limit theorems for certain diffusion processes with interaction, 1984. ,
DOI : 10.1016/s0924-6509(08)70405-7
Prédire n'est pas expliquer. Flammarion, 2009. ,
On the dynamics of mean field equations for stochastic neural fields with delays, 2011. ,
Propagation of chaos in neural fields, The Annals of Applied Probability, vol.24, issue.3, 2011. ,
DOI : 10.1214/13-AAP950
URL : https://hal.archives-ouvertes.fr/hal-00942210
Integral Equations, p.147, 1957. ,
Neural Synchrony in Brain Disorders: Relevance for Cognitive Dysfunctions and Pathophysiology, Neuron, vol.52, issue.1, pp.155-168, 2006. ,
DOI : 10.1016/j.neuron.2006.09.020
Chaos in neuronal networks with balanced excitatory and inhibitory activity, Science, issue.5293, pp.2741724-1726, 1996. ,
Limite de champ moyen, 2001. ,
Randomness in neurons: a multiscale probabilistic analysis, Bibliography, 2010. ,
Computational Neuroscience in Epilepsy, chapter Transition to Ictal Activity in Temporal Lobe Epilepsy: Insights from Macroscopic Models, p.136, 2008. ,
Channel noise in neurons, Trends in Neurosciences, vol.23, issue.3, pp.131-137, 2000. ,
DOI : 10.1016/S0166-2236(99)01521-0
Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs, Nature, vol.373, issue.6509, pp.33-36, 1995. ,
DOI : 10.1038/373033a0
Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons, Biophysical Journal, vol.12, issue.1, pp.1-24, 1972. ,
DOI : 10.1016/S0006-3495(72)86068-5
A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Kybernetik, vol.12, issue.2, pp.55-80, 1973. ,
DOI : 10.1007/BF00288786
Voltage fluctuations in neurons: signal or noise? Physiological Review, pp.917-929, 2011. ,