Random Dynamical Systems, 1998. ,
Glutamate decarboxylase-immunoreactive neurons are preserved in human epileptic hippocampus, J Neurosci, vol.9, issue.7, pp.2562-2574, 1989. ,
Cellular and network mechanisms of electrographic seizures. Drug Discovery Today: Disease Models, pp.45-57, 2008. ,
Methodology of stereo EEG exploration and surgical intervention in epilepsy, Rev. Otoneuroophtalmol, vol.45, issue.4, pp.315-343, 1973. ,
Noise-induced phenomena in slow-fast dynamical systems, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00010168
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
Cortex: Statistics and Geometry of Neuronal Connectivity, 1998. ,
DOI : 10.1007/978-3-662-03733-1
Stereoelectroencephalography, Multimethodological assessment of the epileptic forms, pp.80-108, 1996. ,
Evaluation of different measures of functional connectivity using a neural mass model, NeuroImage, vol.21, issue.2, pp.659-673, 2004. ,
DOI : 10.1016/j.neuroimage.2003.10.006
A neural mass model for MEG/EEG:, NeuroImage, vol.20, issue.3, pp.1743-1755, 2003. ,
DOI : 10.1016/j.neuroimage.2003.07.015
Theoretical Neuroscience : Computational and Mathematical Modeling of Neural Systems, 2001. ,
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
Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3, Ergodic Theory and Dynamical Systems, pp.375-413, 1987. ,
DOI : 10.1016/0001-8708(75)90048-1
Bifurcations of planar vector fields(nilpotent singularities and abelian integrals), 1991. ,
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
Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, Society for Industrial Mathematics, 2002. ,
DOI : 10.1137/1.9780898718195
Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation, SIAM Journal on Applied Mathematics, vol.46, issue.2, pp.233-253, 1986. ,
DOI : 10.1137/0146017
A constructive mean-field analysis of multi population neural networks with random synaptic weights and stochastic inputs, Frontiers in Computational Neuroscience, vol.3, issue.1, 2009. ,
DOI : 10.3389/neuro.10.001.2009
URL : https://hal.archives-ouvertes.fr/inria-00258345
A model of the olfactory system, Neural Modeling, pp.41-62, 1973. ,
Mass action in the nervous system, 1975. ,
Simulation of chaotic EEG patterns with a dynamic model of the olfactory system, Biological Cybernetics, vol.52, issue.2-3, pp.139-150, 1987. ,
DOI : 10.1007/BF00317988
Mathematical formulations of Hebbian learning, Biological Cybernetics, vol.87, issue.5-6, pp.404-415, 2002. ,
DOI : 10.1007/s00422-002-0353-y
Singularities and Groups in Bifurcation Theory, volume I, 1984. ,
Singularities and Groups in Bifurcation Theory, volume II, 1988. ,
Bifurcation Analysis of Jansen's Neural Mass Model, Neural Computation, vol.18, issue.12, pp.3052-3068, 2006. ,
DOI : 10.1007/s004220000160
Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 1983. ,
Computing Hopf Bifurcations. II: Three Examples From Neurophysiology, SIAM Journal on Scientific Computing, vol.17, issue.6, pp.1275-1301, 1996. ,
DOI : 10.1137/S1064827593253495
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.1609
Computing Hopf Bifurcations I, SIAM Journal on Numerical Analysis, vol.34, issue.1, 1996. ,
DOI : 10.1137/S0036142993253461
Extracellular free calcium and potassium during paroxysmal activity in the cerebral cortex of the cat, Experimental Brain Research, vol.27, issue.3-4, pp.237-243 ,
DOI : 10.1007/BF00235500
Vulnerability and plasticity of the GABA system in the pilocarpine model of spontaneous recurrent seizures, Epilepsy Research, vol.26, issue.1, pp.207-218, 1996. ,
DOI : 10.1016/S0920-1211(96)00054-X
Shape and arrangement of columns in cat's striate cortex, The Journal of Physiology, vol.165, issue.3, p.559, 1963. ,
DOI : 10.1113/jphysiol.1963.sp007079
Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat, Journal of Neurophysiology, vol.28, pp.229-289, 1965. ,
NEURAL EXCITABILITY, SPIKING AND BURSTING, International Journal of Bifurcation and Chaos, vol.10, issue.06, pp.1171-1266, 2000. ,
DOI : 10.1142/S0218127400000840
Simple model of spiking neurons, IEEE Transactions on Neural Networks, vol.14, issue.6, pp.1569-1572, 2003. ,
DOI : 10.1109/TNN.2003.820440
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
A neurophysiologically-based mathematical model of flash visual evoked potentials, Biological Cybernetics, vol.31, issue.3, pp.275-283, 1993. ,
DOI : 10.1007/BF00224863
Review of the role of inhibitory neurons in chronic epileptic foci induced by intracerebral tetanus toxin, Epilepsy Research, vol.26, issue.1, pp.59-66, 1996. ,
DOI : 10.1016/S0920-1211(96)00040-X
Principles of Neural Science, 2000. ,
Algorithm for Evaluation of Complex Bifurcation Points in Ordinary Differential Equations, SIAM Journal on Applied Mathematics, vol.38, issue.1, pp.103-107, 1980. ,
DOI : 10.1137/0138008
Elements of Applied Bifurcation Theory, Applied Mathematical Sciences, 1998. ,
How do seizures stop? Epilepsia, pp.1651-1664 ,
DOI : 10.1111/j.1528-1167.2008.01669.x
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2738747
Model of brain rhythmic activity, Kybernetik, vol.1, issue.1, pp.27-37, 1974. ,
DOI : 10.1007/BF00270757
Models of Neuronal Populations: The Basic Mechanisms of Rhythmicity, 1976. ,
DOI : 10.1016/S0079-6123(08)60995-4
MRI-negative prefrontal epilepsy due to cortical dysplasia explored by stereoelectroencephalography (SEEG), Epileptic Disord, vol.10, issue.4, pp.330-339, 2008. ,
Modality and topographic properties of single neurons of cat's somatosensory cortex, Journal of Neurophysiology, vol.20, pp.408-434, 1957. ,
Cation-Chloride Cotransporters and GABA-ergic Innervation in the Human Epileptic Hippocampus, Epilepsia, vol.557, issue.4, pp.663-673, 2007. ,
DOI : 10.1016/S0006-8993(01)02649-X
Targeting Epilepsy Genes, Neuron, vol.16, issue.2, pp.241-244, 1996. ,
DOI : 10.1016/S0896-6273(00)80042-2
Analysis of neural excitability and oscillations, 1989. ,
Role of Delays in Shaping Spatiotemporal Dynamics of Neuronal Activity in Large Networks, Physical Review Letters, vol.94, issue.23, p.94238103, 2005. ,
DOI : 10.1103/PhysRevLett.94.238103
URL : https://hal.archives-ouvertes.fr/hal-00094058
Nonlinear dynamics and chaos, 1994. ,
Dynamics of Epileptic Phenomena Determined From Statistics of Ictal Transitions, IEEE Transactions on Biomedical Engineering, vol.53, issue.3, pp.524-532, 2006. ,
DOI : 10.1109/TBME.2005.869800
Unmasking recurrent excitation generated by mossy fiber sprouting in the epileptic dentate gyrus: an emergent property of a complex system, Prog Brain Res, vol.163, pp.541-563, 2007. ,
DOI : 10.1016/S0079-6123(07)63029-5
Pathophysiology of Neocortical Epileptic Seizures, Atlas of epilepsies, chapter 27, pp.203-212, 2010. ,
DOI : 10.1007/978-1-84882-128-6_27
Neocortical seizures: initiation, development and cessation, Neuroscience, vol.123, issue.2, pp.299-336, 2004. ,
DOI : 10.1016/j.neuroscience.2003.08.051
Bifurcation Analysis of a General Class of Nonlinear Integrate-and-Fire Neurons, SIAM Journal on Applied Mathematics, vol.68, issue.4, pp.1045-1079, 2008. ,
DOI : 10.1137/070687268
URL : https://hal.archives-ouvertes.fr/inria-00142987
Dynamics and bifurcations of the adaptive exponential integrate-and-fire model, Biological Cybernetics, vol.62, issue.5, pp.4-5319, 2008. ,
DOI : 10.1007/s00422-008-0267-4
URL : https://hal.archives-ouvertes.fr/inria-00422701
Spiking Dynamics of Bidimensional Integrate-and-Fire Neurons, SIAM Journal on Applied Dynamical Systems, vol.8, issue.4, pp.1462-1506, 2009. ,
DOI : 10.1137/080742762
URL : https://hal.archives-ouvertes.fr/inria-00276924
Neocortical pyramidal cells: a model with dendritic calcium conductance reproduces repetitive firing and epileptic behavior, Brain Research, vol.173, issue.2, pp.243-57, 1979. ,
DOI : 10.1016/0006-8993(79)90625-5
Simulation of intrinsic bursting in CA3 hippocampal neurons, Neuroscience, vol.7, issue.5, pp.1233-1275, 1982. ,
DOI : 10.1016/0306-4522(82)91130-7
Hippocampal pyramidal cells: significance of dendritic ionic conductances for neuronal function and epileptogenesis, Journal of Neurophysiology, vol.42, issue.2, pp.476-496, 1979. ,
A Possible Role for Gap Junctions in Generation of Very Fast EEG Oscillations Preceding the Onset of, and Perhaps Initiating, Seizures, Epilepsia, issue.2, pp.42153-170, 2001. ,
A model of the spatial-temporal characteristics of the alpha rhythm, Bulletin of Mathematical Biology, vol.31, issue.No. 1, pp.283-305, 1982. ,
DOI : 10.1007/BF02463252
Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition, European Journal of Neuroscience, vol.38, issue.9, pp.1499-1508, 2002. ,
DOI : 10.1007/s004220050191
Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals, Biological Cybernetics, vol.83, issue.4, pp.367-378, 2000. ,
DOI : 10.1007/s004220000160
Transition to Ictal Activity in Temporal Lobe Epilepsy, Computational Neuroscience in Epilepsy, pp.356-386, 2008. ,
DOI : 10.1016/B978-012373649-9.50026-0
Interictal to ictal transition in human temporal lobe epilepsy: insights from a computational model of intracerebral EEG, J Clin Neurophysiol, vol.22, issue.5, pp.343-356, 2005. ,
URL : https://hal.archives-ouvertes.fr/inserm-00147326
Networks of interneurons with fast and slow gamma -aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gamma-theta rhythm, Proceedings of the National Academy of Sciences, vol.97, issue.14, pp.978128-8133, 2000. ,
DOI : 10.1073/pnas.100124097
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
Performance of a model for a local neuron population, Biological Cybernetics, vol.1, issue.1, pp.15-26, 1978. ,
DOI : 10.1007/BF00337367