P. Hartman, A lemma in the theory of structural stability of differential equations, Proceedings of the American Mathematical Society, vol.11, issue.4, pp.610-620, 1960.
DOI : 10.1090/S0002-9939-1960-0121542-7

D. M. Grobman, Homeomorphisms of systems of differential equations, Dokl. Akad. Nauk SSSR, vol.128, pp.880-881, 1959.

J. A. Carrillo, S. Cordier, and S. Mancini, A decision-making Fokker???Planck model in computational neuroscience, Journal of Mathematical Biology, vol.53, issue.1, pp.801-830, 2011.
DOI : 10.1007/s00285-010-0391-3

URL : https://hal.archives-ouvertes.fr/hal-00452994

J. A. Carrillo, S. Cordier, G. Deco, and S. Mancini, General One- Dimensional Fokker-Planck Reduction of Rate-equations models for twochoice decision making, 2011.

N. Berglund and B. Gentz, Noise-Induced Phenomena in Slow-Fast Dynamical Systems. A Sample-Paths Approach, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00010168

N. Brunel, Dynamics of sparsely connected networks of excitatory and inhibitory spiking networks, Journal of Computational Neuroscience, vol.8, issue.3, pp.183-208, 2000.
DOI : 10.1023/A:1008925309027

N. Brunel and V. Hakim, 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

N. Brunel and X. Wang, What Determines the Frequency of Fast Network Oscillations With Irregular Neural Discharges? I. Synaptic Dynamics and Excitation-Inhibition Balance, Journal of Neurophysiology, vol.90, issue.1, pp.415-430, 2003.
DOI : 10.1152/jn.01095.2002

D. Cai, L. Tao, and D. W. Mclaughlin, An embedded network approach for scale-up of fluctuation-driven systems with preservation of spike information, Proceedings of the National Academy of Sciences, vol.101, issue.39, pp.14288-14293, 2004.
DOI : 10.1073/pnas.0404062101

D. Cai, L. Tao, A. V. Rangan, and D. W. Mclaughlin, Kinetic theory for neuronal network dynamics, Communications in Mathematical Sciences, vol.4, issue.1, pp.97-127, 2006.
DOI : 10.4310/CMS.2006.v4.n1.a4

D. Cai, L. Tao, M. J. Shelley, and D. W. Mclaughlin, An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex, Proceedings of the National Academy of Sciences, vol.101, issue.20, pp.7757-7762, 2004.
DOI : 10.1073/pnas.0401906101

G. Deco and D. Martí, Deterministic analysis of stochastic bifurcations in multi-stable neurodynamical systems, Biological Cybernetics, vol.100, issue.3, pp.487-496, 2007.
DOI : 10.1007/s00422-007-0144-6

L. Camera, G. Rauch, A. Luescher, H. Senn, W. Fusi et al., ???Like Input Currents, Neural Computation, vol.79, issue.10, pp.2101-2124, 2004.
DOI : 10.1016/S0022-5193(83)80013-7

C. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 1985.

A. Renart, N. Brunel, and X. Wang, Computational Neuroscience: A Comprehensive Approach, 2003.

A. Roxin and A. Ledberg, Neurobiological Models of Two-Choice Decision Making Can Be Reduced to a One-Dimensional Nonlinear Diffusion Equation, PLoS Computational Biology, vol.54, issue.3, pp.43-100, 2008.
DOI : 10.1371/journal.pcbi.1000046.s001

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