L. Arnold, Random Dynamical Systems, 1998.

T. L. Babb, J. K. Pretorius, W. R. Kupfer, and P. H. Crandall, Glutamate decarboxylase-immunoreactive neurons are preserved in human epileptic hippocampus, J Neurosci, vol.9, issue.7, pp.2562-2574, 1989.

M. Bazhenov, I. Timofeev, F. Fröhlich, and T. Sejnowski, Cellular and network mechanisms of electrographic seizures. Drug Discovery Today: Disease Models, pp.45-57, 2008.

J. Bancaud and J. Talairach, Methodology of stereo EEG exploration and surgical intervention in epilepsy, Rev. Otoneuroophtalmol, vol.45, issue.4, pp.315-343, 1973.

N. Berglund and B. Gentz, Noise-induced phenomena in slow-fast dynamical systems, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00010168

G. Bettus, F. Wendling, M. Guye, L. Valton, J. Régis et al., 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

V. Braitenberg and A. Schüz, Cortex: Statistics and Geometry of Neuronal Connectivity, 1998.
DOI : 10.1007/978-3-662-03733-1

P. Chauvel, J. Vignal, A. Biraben, J. Badier, and J. Scarabin, Stereoelectroencephalography, Multimethodological assessment of the epileptic forms, pp.80-108, 1996.

O. David, D. Cosmelli, and K. J. Friston, 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

O. David and K. J. Friston, A neural mass model for MEG/EEG:, NeuroImage, vol.20, issue.3, pp.1743-1755, 2003.
DOI : 10.1016/j.neuroimage.2003.07.015

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

A. Dhooge, W. Govaerts, and Y. Kuznetsov, 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

A. Dhooge, W. Govaerts, and Y. A. Kuznetsov, MATCONT, ACM Transactions on Mathematical Software, vol.29, issue.2, pp.141-164, 2003.
DOI : 10.1145/779359.779362

F. Dumortier, R. Roussarie, and J. Sotomayor, 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

F. Dumortier, R. Roussarie, J. Sotomayor, and H. Zoladek, Bifurcations of planar vector fields(nilpotent singularities and abelian integrals), 1991.

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

B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, Society for Industrial Mathematics, 2002.
DOI : 10.1137/1.9780898718195

G. B. Ermentrout and N. Kopell, 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

O. Faugeras, J. Touboul, C. , and B. , 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

W. Freeman, A model of the olfactory system, Neural Modeling, pp.41-62, 1973.

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

W. Freeman, 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

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

M. Golubitsky and D. Schaeffer, Singularities and Groups in Bifurcation Theory, volume I, 1984.

M. Golubitsky, I. Stewart, and D. Schaeffer, Singularities and Groups in Bifurcation Theory, volume II, 1988.

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

J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 1983.

J. Guckenheimer and M. Myers, 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

J. Guckenheimer, M. Myers, and B. Sturmfels, Computing Hopf Bifurcations I, SIAM Journal on Numerical Analysis, vol.34, issue.1, 1996.
DOI : 10.1137/S0036142993253461

U. Heinemann, H. D. Lux, and M. J. Gutnick, 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

C. R. Houser and M. Esclapez, 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

D. Hubel and T. Wiesel, 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

D. Hubel and T. Wiesel, 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.

E. Izhikevich, NEURAL EXCITABILITY, SPIKING AND BURSTING, International Journal of Bifurcation and Chaos, vol.10, issue.06, pp.1171-1266, 2000.
DOI : 10.1142/S0218127400000840

E. Izhikevich, Simple model of spiking neurons, IEEE Transactions on Neural Networks, vol.14, issue.6, pp.1569-1572, 2003.
DOI : 10.1109/TNN.2003.820440

B. H. Jansen and V. G. 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

B. H. Jansen, G. Zouridakis, and M. E. Brandt, A neurophysiologically-based mathematical model of flash visual evoked potentials, Biological Cybernetics, vol.31, issue.3, pp.275-283, 1993.
DOI : 10.1007/BF00224863

J. Jefferys and M. Whittington, 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

E. Kandel, J. Schwartz, and T. Jessel, Principles of Neural Science, 2000.

M. Kubicek, 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

Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Applied Mathematical Sciences, 1998.

F. A. Lado and S. L. Moshé, 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

F. Lopes-da-silva, A. Hoeks, and L. Zetterberg, Model of brain rhythmic activity, Kybernetik, vol.1, issue.1, pp.27-37, 1974.
DOI : 10.1007/BF00270757

F. Lopes-da-silva, A. Van-rotterdam, P. Barts, E. Van-heusden, and W. Burr, Models of Neuronal Populations: The Basic Mechanisms of Rhythmicity, 1976.
DOI : 10.1016/S0079-6123(08)60995-4

A. Mcgonigal, M. Gavaret, A. Da-fonseca, M. Guye, D. Scavarda et al., MRI-negative prefrontal epilepsy due to cortical dysplasia explored by stereoelectroencephalography (SEEG), Epileptic Disord, vol.10, issue.4, pp.330-339, 2008.

V. Mountcastle, Modality and topographic properties of single neurons of cat's somatosensory cortex, Journal of Neurophysiology, vol.20, pp.408-434, 1957.

A. Munoz, P. Mendez, J. Defelipe, and F. J. Alvarez-leefmans, 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

J. L. Noebels, Targeting Epilepsy Genes, Neuron, vol.16, issue.2, pp.241-244, 1996.
DOI : 10.1016/S0896-6273(00)80042-2

J. Rinzel and B. Ermentrout, Analysis of neural excitability and oscillations, 1989.

A. Roxin, N. Brunel, H. , and D. , 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

S. Strogatz, Nonlinear dynamics and chaos, 1994.

P. Suffczynski, F. Lopes-da-silva, J. Parra, D. Velis, B. Bouwman et al., 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

T. P. Sutula and F. E. Dudek, 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

I. Timofeev, Pathophysiology of Neocortical Epileptic Seizures, Atlas of epilepsies, chapter 27, pp.203-212, 2010.
DOI : 10.1007/978-1-84882-128-6_27

I. Timofeev and M. Steriade, Neocortical seizures: initiation, development and cessation, Neuroscience, vol.123, issue.2, pp.299-336, 2004.
DOI : 10.1016/j.neuroscience.2003.08.051

J. Touboul, 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

J. Touboul and R. Brette, 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

J. Touboul and R. Brette, 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

R. Traub, 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

R. Traub, 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

R. Traub and R. Llinas, Hippocampal pyramidal cells: significance of dendritic ionic conductances for neuronal function and epileptogenesis, Journal of Neurophysiology, vol.42, issue.2, pp.476-496, 1979.

R. Traub, M. Whittington, E. Buhl, F. Lebeau, A. Bibbig et al., 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. 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, pp.283-305, 1982.
DOI : 10.1007/BF02463252

F. Wendling, F. Bartolomei, J. Bellanger, and P. Chauvel, 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

F. Wendling, J. Bellanger, F. Bartolomei, and P. Chauvel, 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

F. Wendling and P. Chauvel, Transition to Ictal Activity in Temporal Lobe Epilepsy, Computational Neuroscience in Epilepsy, pp.356-386, 2008.
DOI : 10.1016/B978-012373649-9.50026-0

F. Wendling, A. Hernandez, J. Bellanger, P. Chauvel, and F. Bartolomei, 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

J. A. White, M. I. Banks, R. A. Pearce, and N. J. Kopell, 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

H. Wilson and J. Cowan, 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

H. Wilson and J. Cowan, 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

L. Zetterberg, L. Kristiansson, and K. Mossberg, Performance of a model for a local neuron population, Biological Cybernetics, vol.1, issue.1, pp.15-26, 1978.
DOI : 10.1007/BF00337367