O. Arino, E. A. Hbid, and . Dads, Delay differential equations and applications, 2006.
DOI : 10.1007/1-4020-3647-7

O. Arino and E. Sanchez, Linear Theory of Abstract Functional Differential Equations of Retarded Type, Journal of Mathematical Analysis and Applications, vol.191, issue.3, pp.547-571, 1995.
DOI : 10.1006/jmaa.1995.1148

M. Fatihcan, A. Atay, and . Hutt, Stability and bifurcations in neural fields with finite propagation speed and general connectivity, SIAM Journal on Applied Mathematics, vol.65, issue.2, pp.644-666, 2005.

M. Fatihcan, A. Atay, and . Hutt, Neural fields with distributed transmission speeds and long-range feedback delays, SIAM Journal of Applied Dynamical Systems, vol.5, issue.4, pp.670-698, 2006.

A. Bátkai and S. Piazzera, Semigroups for delay equations, 2005.

R. Ben-yishai, R. Bar-or, and H. Sompolinsky, Theory of orientation tuning in visual cortex., Proceedings of the National Academy of Sciences, pp.3844-3848, 1995.
DOI : 10.1073/pnas.92.9.3844

I. Bojak and D. T. Liley, Axonal Velocity Distributions in Neural Field Equations, PLoS Computational Biology, vol.796, issue.1, 2010.
DOI : 10.1371/journal.pcbi.1000653.s001

P. C. Bressloff, N. W. Bressloff, and J. D. Cowan, Dynamical Mechanism for Sharp Orientation Tuning in an Integrate-and-Fire Model of a Cortical Hypercolumn, Neural Computation, vol.16, issue.11, pp.2473-2511, 2000.
DOI : 10.1007/BF00288786

P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas, and M. C. Wiener, Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.356, issue.1407, pp.306299-330, 1407.
DOI : 10.1098/rstb.2000.0769

P. C. Bressloff and Z. P. Kilpatrick, Nonlocal Ginzburg-Landau equation for cortical pattern formation, Physical Review E, vol.78, issue.4, pp.419161-419177, 2008.
DOI : 10.1103/PhysRevE.78.041916

P. Clément, O. Diekmann, M. Gyllenberg, H. Heijmans, and H. Thieme, Perturbation theory for dual semigroups, Mathematische Annalen, vol.3, issue.4, pp.709-725, 1988.
DOI : 10.1007/BF01457866

B. D. Coleman and V. J. , Norms and semi-groups in the theory of fading memory Archive for Rational Mechanics and Analysis, pp.87-123, 1966.

S. Coombes, N. Venkov, L. Shiau, I. Bojak, D. T. Liley et al., Modeling electrocortical activity through improved local approximations of integral neural field equations, Physical Review E, vol.76, issue.5, p.7651901, 2007.
DOI : 10.1103/PhysRevE.76.051901

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

O. Diekmann, Delay equations: functional-, complex-, and nonlinear analysis, 1995.
DOI : 10.1007/978-1-4612-4206-2

O. Diekmann and S. Van-gils, The center manifold for delay equations in the light of suns and stars. Singularity Theory and its Applications, pp.122-141, 1991.

N. Dunford and J. T. Schwartz, Linear operators: Spectral operators, 1988.

K. J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Semigroup Forum, vol.63, issue.2, 2001.
DOI : 10.1007/s002330010042

G. B. Ermentrout and J. D. Cowan, Large Scale Spatially Organized Activity in Neural Nets, SIAM Journal on Applied Mathematics, vol.38, issue.1, pp.1-21, 1980.
DOI : 10.1137/0138001

T. Faria, Normal forms for semilinear functional differential equations in Banach spaces and applications. Part II, Discrete and Continuous Dynamical Systems (DCDS-A), pp.155-176, 2001.
DOI : 10.3934/dcds.2001.7.155

T. Faria, W. Huang, and J. Wu, Smoothness of Center Manifolds for Maps and Formal Adjoints for Semilinear FDEs in General Banach Spaces, SIAM Journal on Mathematical Analysis, vol.34, issue.1, p.173, 2002.
DOI : 10.1137/S0036141001384971

T. Faria and L. Magalhaes, Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation, Journal of Differential Equations, vol.122, issue.2, pp.181-200, 1995.
DOI : 10.1006/jdeq.1995.1144

]. O. Faugeras, F. Grimbert, and J. Slotine, Abolute stability and complete synchronization in a class of neural fields models, SIAM Journal of Applied Mathematics, vol.61, issue.1, pp.205-250, 2008.

J. K. Hale and S. M. , Introduction to functional differential equations, 1993.
DOI : 10.1007/978-1-4612-4342-7

M. Haragus and G. Iooss, Local bifurcations, center manifolds, and normal forms in infinite dimensional systems, EDP Sci, 2010.
DOI : 10.1007/978-0-85729-112-7
URL : https://hal.archives-ouvertes.fr/hal-00877080

H. J. Hupkes and S. M. , Center Manifold Theory for Functional Differential Equations of Mixed Type, Journal of Dynamics and Differential Equations, vol.105, issue.2, pp.497-560, 2007.
DOI : 10.1007/s10884-006-9055-9

A. Hutt, Local excitation-lateral inhibition interaction yields oscillatory instabilities in nonlocally interacting systems involving finite propagation delay, Physics Letters A, vol.372, issue.5, pp.541-546, 2008.
DOI : 10.1016/j.physleta.2007.08.018
URL : https://hal.archives-ouvertes.fr/inria-00332987

A. Hutt, Finite propagation speeds in spatially extended systems. Complex Time-Delay Systems: Theory and Applications, p.151, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00403132

G. Iooss and K. Kirchgassner, Travelling Waves in a Chain??of Coupled Nonlinear Oscillators, Communications in Mathematical Physics, vol.211, issue.2, pp.439-464, 2000.
DOI : 10.1007/s002200050821
URL : https://hal.archives-ouvertes.fr/hal-01271086

V. Jirsa and J. Kelso, Spatiotemporal pattern formation in neural systems with heterogeneous connection topologies, Physical Review E, vol.62, issue.6, pp.8462-8465, 2000.
DOI : 10.1103/PhysRevE.62.8462

T. Kato, Perturbation Theory for Linear Operators, 1995.

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

V. Markounikau, C. Igel, A. Grinvald, and D. Jancke, A Dynamic Neural Field Model of Mesoscopic Cortical Activity Captured with Voltage-Sensitive Dye Imaging, PLoS Computational Biology, vol.55, issue.46, p.1000919, 2010.
DOI : 10.1371/journal.pcbi.1000919.s001

S. Nakagiri, Structural properties of functional differential equations in banach spaces, Osaka J. Math, vol.25, pp.353-398, 1988.

S. I. Nakagiri, Optimal control of linear retarded systems in Banach spaces, Journal of Mathematical Analysis and Applications, vol.120, issue.1, pp.169-210, 1986.
DOI : 10.1016/0022-247X(86)90210-6

D. J. Pinto, J. C. Brumberg, D. J. Simons, G. B. Ermentrout, and R. Traub, A quantitative population model of whisker barrels: Re-examining the Wilson-Cowan equations, Journal of Computational Neuroscience, vol.31, issue.3, pp.247-264, 1996.
DOI : 10.1007/BF00161134

V. A. Pliss, The reduction principle in the theory of the stability of motion, Izv. Akad. Nauk SSSR, Ser Mat, issue.27, pp.1297-1324, 1964.

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

A. Roxin and E. Montbrió, How effective delays shape oscillatory dynamics in neuronal networks, Physica D: Nonlinear Phenomena, vol.240, issue.3, pp.323-345, 2011.
DOI : 10.1016/j.physd.2010.09.009

C. Travis and G. Webb, Existence and stability for partial functional differential equations, 1974.

A. Vanderbauwhede and G. Iooss, Center Manifold Theory in Infinite Dimensions, Dynamics Reported PJ-Expositions in Dynamical Systems, vol.1, p.125, 1992.
DOI : 10.1007/978-3-642-61243-5_4

A. Vanderbauwhede and S. Van-gils, Center manifolds and contractions on a scale of Banach spaces, Journal of Functional Analysis, vol.72, issue.2, pp.209-224, 1987.
DOI : 10.1016/0022-1236(87)90086-3

R. Veltz, An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays, Comptes Rendus Mathematique, vol.349, issue.13-14, pp.749-752, 2011.
DOI : 10.1016/j.crma.2011.06.014
URL : https://hal.archives-ouvertes.fr/hal-00845727

R. Veltz and O. Faugeras, Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations, SIAM Journal on Applied Dynamical Systems, vol.9, issue.3, pp.954-998, 2010.
DOI : 10.1137/090773611
URL : https://hal.archives-ouvertes.fr/hal-00712201

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

G. Webb, Functional differential equations and nonlinear semigroups in Lp-spaces, Journal of Differential Equations, vol.20, issue.1, pp.71-89, 1976.
DOI : 10.1016/0022-0396(76)90097-8

J. Wu, Theory and applications of partial functional differential equations, 1996.
DOI : 10.1007/978-1-4612-4050-1

J. Wu, Symmetric functional differential equations and neural networks with memory. Transactions of the, pp.4799-4838, 1998.

K. Yosida, Functional Analysis, volume XII of Grundlehren der mathematischen Wissenschaften, 1980.