F. M. Atay and A. Hutt, Neural Fields with Distributed Transmission Speeds and Long???Range Feedback Delays, SIAM Journal on Applied Dynamical Systems, vol.5, issue.4, pp.670-698, 2006.
DOI : 10.1137/050629367

P. Beim-graben and A. Hutt, Attractor and saddle node dynamics in heterogeneous neural fields, EPJ Nonlinear Biomedical Physics, vol.12, issue.20, 2014.
DOI : 10.1140/epjnbp17

URL : https://hal.archives-ouvertes.fr/hal-00987789

C. Brackley and M. Turner, Persistent fluctuations of activity in undriven continuum neural field models with power-law connections, Physical Review E, vol.79, issue.1, p.79, 2009.
DOI : 10.1103/PhysRevE.79.011918

P. Bressloff, Spatiotemporal dynamics of continuum neural fields, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.3, pp.45-033001, 2012.
DOI : 10.1088/1751-8113/45/3/033001

P. C. Bressloff, Traveling fronts and wave propagation failure in an inhomogeneous neural network, Physica D: Nonlinear Phenomena, vol.155, issue.1-2, pp.83-100, 2001.
DOI : 10.1016/S0167-2789(01)00266-4

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

E. Buckwar and R. Winkler, Multistep methods for SDEs and their application to problems with small noise, SIAM Journal on Numerical Analysis, vol.44, issue.2, pp.779-803, 2006.
DOI : 10.1137/040602857

E. Buckwar and R. Winkler, Multi-Step Maruyama Methods for Stochastic Delay Differential Equations, Stochastic Analysis and Applications, vol.14, issue.5, pp.933-959, 2007.
DOI : 10.1016/S0377-0427(03)00436-9

E. Buckwar, R. Kuske, S. Mohammed, and T. Shardlow, Abstract, LMS Journal of Computation and Mathematics, vol.70, pp.60-99, 2008.
DOI : 10.1214/105051606000000060

M. Carletti, Numerical solution of stochastic differential problems in the biosciences, Journal of Computational and Applied Mathematics, vol.185, issue.2, pp.422-440, 2006.
DOI : 10.1016/j.cam.2005.03.020

N. Carnevale and M. Hines, The NEURON Book, Cambridge UK, 2006.
DOI : 10.1017/CBO9780511541612

S. Coombes, Waves, bumps, and patterns in neural field theories, Biological Cybernetics, vol.16, issue.2, pp.91-108, 2005.
DOI : 10.1007/s00422-005-0574-y

S. Coombes and M. Owen, Bumps, Breathers, and Waves in a Neural Network with Spike Frequency Adaptation, Physical Review Letters, vol.94, issue.14, p.148102, 2005.
DOI : 10.1103/PhysRevLett.94.148102

S. Coombes, C. Laing, H. Schmidt, N. Svanstedt, and J. Wyller, Waves in random neural media, Discrete and Continuous Dynamical Systems, vol.32, issue.8, pp.2951-2970, 2012.
DOI : 10.3934/dcds.2012.32.2951

S. Coombes and P. Beim-graben, Neural Fields: Theory and Applications, 2014.

G. Deco, V. Jirsa, P. Robinson, M. Breakspear, and K. Friston, The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields, PLoS Computational Biology, vol.355, issue.2, p.1000092, 2008.
DOI : 10.1371/journal.pcbi.1000092.t001

H. Demeulemeester, F. Vandesande, G. Orban, C. Brandon, and J. Vanderhaeghen, Heterogeneity of gabaergic cells in cat visual cortex, J. Neurosci, vol.8, issue.3, pp.988-1000, 1988.

A. J. Elvin, C. R. Laing, and M. G. Roberts, Transient Turing patterns in a neural field model, Physical Review E, vol.79, issue.1, pp.79-011911, 2009.
DOI : 10.1103/PhysRevE.79.011911

G. Faye and O. Faugeras, Some theoretical and numerical results for delayed neural field equations, Physica D: Nonlinear Phenomena, vol.239, issue.9, pp.561-578, 2010.
DOI : 10.1016/j.physd.2010.01.010

URL : https://hal.archives-ouvertes.fr/hal-00847433

S. Folias and P. Bressloff, Breathers in Two-Dimensional Neural Media, Physical Review Letters, vol.95, issue.20, 2005.
DOI : 10.1103/PhysRevLett.95.208107

K. Friston, J. Kahan, B. Biswal, and A. Razi, A DCM for resting state fMRI, NeuroImage, vol.94, pp.94-396407, 2014.
DOI : 10.1016/j.neuroimage.2013.12.009

M. Hashemi, A. Hutt, and J. Sleigh, Anesthetic action on extrasynaptic receptors: effects in neural population models of EEG activity, J. Front. Syst. Neurosci, vol.8, issue.232, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01088062

A. Hutt, Generalization of the reaction-diffusion, Swift-Hohenberg, and Kuramoto-Sivashinsky equations and effects of finite propagation speeds, Physical Review E, vol.75, issue.2, pp.75-026214, 2007.
DOI : 10.1103/PhysRevE.75.026214

A. Hutt, Oscillatory activity in excitable neural systems, Contemporary Physics, vol.202, issue.1, pp.3-16, 2009.
DOI : 10.1109/TMI.2002.1009385

URL : https://hal.archives-ouvertes.fr/inria-00434441

A. Hutt and F. Atay, Effects of distributed transmission speeds on propagating activity in neural populations, Physical Review E, vol.73, issue.2, pp.73-021906, 2006.
DOI : 10.1103/PhysRevE.73.021906

A. Hutt and L. Buhry, Study of GABAergic extra-synaptic tonic inhibition in single neurons and neural populations by traversing neural scales: application to propofol-induced anaesthesia, Journal of Computational Neuroscience, vol.7, issue.20, pp.417-437, 2014.
DOI : 10.1007/s10827-014-0512-x

URL : https://hal.archives-ouvertes.fr/hal-00916420

A. Hutt and J. Lefebvre, Stochastic center manifold analysis in scalar nonlinear systems involving distributed delays and additive noise, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01006388

A. Hutt and N. Rougier, Numerical Simulation Scheme of One- and Two Dimensional Neural Fields Involving Space-Dependent Delays, Neural Field Theory, pp.175-183, 2014.
DOI : 10.1007/978-3-642-54593-1_6

URL : https://hal.archives-ouvertes.fr/hal-00872132

A. Hutt and N. P. Rougier, Activity spread and breathers induced by finite transmission speeds in two-dimensional neural fields, Physical Review E, vol.82, issue.5, p.55701, 2010.
DOI : 10.1103/PhysRevE.82.055701

URL : https://hal.archives-ouvertes.fr/inria-00533067

A. Hutt, M. Bestehorn, and T. Wennekers, Pattern formation in intracortical neuronal fields, Network: Computation in Neural Systems, vol.14, issue.2, pp.351-368, 2003.
DOI : 10.1088/0954-898X_14_2_310

A. Hutt, C. Sutherland, and A. Longtin, Driving neural oscillations with correlated spatial input and topographic feedback, Physical Review E, vol.78, issue.2, pp.78-021911, 2008.
DOI : 10.1103/PhysRevE.78.021911

URL : https://hal.archives-ouvertes.fr/inria-00332994

M. A. Idiart and L. F. Abbott, Propagation of excitation in neural network models, Network: Computation in Neural Systems, vol.4, issue.3, pp.285-294, 1993.
DOI : 10.1088/0954-898X_4_3_003

V. Jirsa and H. Haken, Field Theory of Electromagnetic Brain Activity, Physical Review Letters, vol.77, issue.5, pp.960-963, 1996.
DOI : 10.1103/PhysRevLett.77.960

V. Jirsa, K. Jantzen, A. Fuchs, and J. Kelso, Spatiotemporal forward solution of the EEG and MEG using network modeling, IEEE Transactions on Medical Imaging, vol.21, issue.5, pp.493-504, 2002.
DOI : 10.1109/TMI.2002.1009385

Z. P. Kilpatrick and P. C. Bressloff, Binocular Rivalry in a Competitive Neural Network with Synaptic Depression, SIAM Journal on Applied Dynamical Systems, vol.9, issue.4, pp.1303-1347, 2010.
DOI : 10.1137/100788872

C. Laing, Spiral Waves in Nonlocal Equations, SIAM Journal on Applied Dynamical Systems, vol.4, issue.3, pp.588-606, 2005.
DOI : 10.1137/040612890

H. P. Langtangen, Numerical Computing in Python, In Python Scripting for Computational Science Texts in Computational Science and Engineering, vol.3, pp.131-181, 2006.
DOI : 10.1007/978-3-540-73916-6_4

B. Molaee-ardekani, L. Senhadji, M. Shamsollahi, B. Vosoughi-vahdat, and E. Wodey, Brain activity modeling in general anesthesia: Enhancing local mean-field models using a slow adaptive firing rate, Physical Review E, vol.76, issue.4, pp.76-041911, 2007.
DOI : 10.1103/PhysRevE.76.041911

URL : https://hal.archives-ouvertes.fr/inserm-00187207

P. Nunez, The brain wave equation: a model for the EEG, Mathematical Biosciences, vol.21, issue.3-4, pp.279-291, 1974.
DOI : 10.1016/0025-5564(74)90020-0

P. Nunez, Toward a quantitative description of large-scale neocortical dynamic function and EEG, Behavioral and Brain Sciences, vol.23, issue.3, pp.371-437, 2000.
DOI : 10.1017/S0140525X00003253

M. R. Owen, C. R. Laing, C. , and S. , Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities, New Journal of Physics, vol.9, issue.10, p.378, 2007.
DOI : 10.1088/1367-2630/9/10/378

D. Pinotsis and K. Friston, Extracting novel information from neuroimaging data using neural fields, EPJ Nonlinear Biomedical Physics, issue.2 5, 2014.
DOI : 10.1140/epjnbp18

URL : http://doi.org/10.1140/epjnbp18

D. Pinotsis, R. Moran, and K. Friston, Dynamic causal modeling with neural fields, NeuroImage, vol.59, issue.2, pp.1261-1274, 2012.
DOI : 10.1016/j.neuroimage.2011.08.020

D. Pinotsis, S. Schwarzkopf, V. Litvak, G. Rees, G. Barnes et al., Dynamic causal modelling of lateral interactions in the visual cortex, NeuroImage, vol.66, pp.563-576, 2013.
DOI : 10.1016/j.neuroimage.2012.10.078

D. Pinto and G. Ermentrout, Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses, SIAM Journal on Applied Mathematics, vol.62, issue.1, pp.206-225, 2001.
DOI : 10.1137/S0036139900346453

M. Qubbaj and V. Jirsa, Neural Field Dynamics with Heterogeneous Connection Topology, Physical Review Letters, vol.98, issue.23, p.238102, 2007.
DOI : 10.1103/PhysRevLett.98.238102

P. Ritter, M. Schirner, A. Mcintosh, and V. Jirsa, The Virtual Brain Integrates Computational Modeling and Multimodal Neuroimaging, Brain Connectivity, vol.3, issue.2, pp.121-145, 2013.
DOI : 10.1089/brain.2012.0120

C. Rosenkilde, Functional heterogeneity of the prefrontal cortex in the monkey: a review, Behavioral and Neural Biology, vol.25, issue.3, pp.301-345, 1979.
DOI : 10.1016/S0163-1047(79)90404-7

C. Rossant and K. D. Harris, Hardware-accelerated interactive data visualization for neuroscience in Python, Frontiers in Neuroinformatics, vol.7, issue.36, 2013.
DOI : 10.3389/fninf.2013.00036

N. Rougier and J. Fix, DANA: distributed numerical and adaptive modelling framework, Network, vol.23, issue.4, pp.237-53, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00718780

N. Rougier and A. Hutt, Synchronous and asynchronous evaluation of dynamic neural fields, Journal of Difference Equations and Applications, vol.12, issue.8, pp.1119-1133, 2011.
DOI : 10.1007/BF00288786

URL : https://hal.archives-ouvertes.fr/inria-00403107

P. Sanz-leona, S. Knock, A. Spiegler, and V. Jirsa, Mathematical framework for large-scale brain network modeling in The Virtual Brain, NeuroImage, vol.111, pp.385-430, 2015.
DOI : 10.1016/j.neuroimage.2015.01.002

H. Schmidt, A. Hutt, and L. Schimansky-geier, Wave fronts in inhomogeneous neural field models, Physica D: Nonlinear Phenomena, vol.238, issue.14, pp.1101-1112, 2009.
DOI : 10.1016/j.physd.2009.02.017

URL : https://hal.archives-ouvertes.fr/inria-00401531

M. L. Steyn-ross, D. A. Steyn-ross, M. T. Wilson, and J. W. Sleigh, Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion, Modeling Phase Transitions in the Brain, pp.271-299, 2010.
DOI : 10.1007/978-1-4419-0796-7_12

M. Stimberg, D. Goodman, V. Benichoux, and R. Brette, Equationoriented specification of neural models for simulations, Front. Neuroinf, vol.8, issue.6, 2014.

A. Turing, The Chemical Basis of Morphogenesis, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.237, issue.641, pp.37-72, 1952.
DOI : 10.1098/rstb.1952.0012

C. Van-loan, Computational Frameworks for the Fast Fourier Transform, 1991.
DOI : 10.1137/1.9781611970999

R. Veltz and O. Faugeras, Stability of the stationary solutions of neural field equations with propagation delays, The Journal of Mathematical Neuroscience, vol.1, issue.1, 2011.
DOI : 10.1186/2190-8567-1-1

URL : https://hal.archives-ouvertes.fr/hal-00784425

R. Veltz and O. Faugeras, A Center Manifold Result for Delayed Neural Fields Equations, SIAM Journal on Mathematical Analysis, vol.45, issue.3, pp.1527-1562, 2013.
DOI : 10.1137/110856162

URL : https://hal.archives-ouvertes.fr/hal-00719794

X. Wang, Neurophysiological and Computational Principles of Cortical Rhythms in Cognition, Physiological Reviews, vol.90, issue.3, pp.1195-1268, 2010.
DOI : 10.1152/physrev.00035.2008

Y. Wang, H. Markram, P. Goodman, T. Berger, J. Ma et al., Heterogeneity in the pyramidal network of the medial prefrontal cortex, Nature Neuroscience, vol.96, issue.4, pp.534-542, 2006.
DOI : 10.1038/nn1670

M. Wertheimer, L. Spillmann, V. Sarris, and R. Sekuler, On Perceived Motion and Figural Organization, 2012.

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

J. Wright and R. Kydd, The electroencephalogram and cortical neural networks, Network: Computation in Neural Systems, vol.3, issue.3, pp.341-362, 1992.
DOI : 10.1088/0954-898X_3_3_006

J. Wright and D. Liley, A millimetric-scale simulation of electrocortical wave dynamics based on anatomical estimates of cortical synaptic density, Network: Computation in Neural Systems, vol.5, issue.2, pp.15-20, 2001.
DOI : 10.1088/0954-898X_5_2_005