L. F. Abbott, Lapicque's introduction of the integrate-and-fire model neuron, Brain Res Bull, vol.50, pp.5-6303, 1907.

L. Alvado, Neurones artificiels sur Silicium: une évolution vers le réseau, pp.1-2674, 2003.

M. A. Arbib, The Handbook of Brain Theory and Neural Networks, 1995.

B. Belhadj, Systèmes neuromorphiques temps réel : contribution à l'intégration de réseaux de neurones biologiquement réalistes avec fonctions de plasticité, pp.81-90, 2010.

G. Bi and M. Poo, Synaptic modification by correlated activity: Hebb's postulate revisited. Annual review of neuroscience, pp.139-166, 2001.

S. Binczak, S. Jacquir, J. Bilbault, V. B. Kazantsev, and V. I. Nekorkin, Experimental study of electrical FitzHugh???Nagumo neurons with modified excitability, Neural Networks, vol.19, issue.5, pp.684-693, 2006.
DOI : 10.1016/j.neunet.2005.07.011
URL : https://hal.archives-ouvertes.fr/hal-00584220

G. Bontorin, S. Renaud, A. Garenne, L. Alvado, L. Masson et al., A Real-Time Closed-Loop Setup for Hybrid Neural Networks, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp.3004-3011, 2007.
DOI : 10.1109/IEMBS.2007.4352961
URL : https://hal.archives-ouvertes.fr/hal-00181426

Y. Bornat, Réseaux de neurones sur silicium : une approche mixte, analogique / numérique, pour l'étude des phénomènes d'adaptation, d'apprentissage et de plasticité, pp.31-39, 2006.

Y. Bornat, J. Tomas, S. Saighi, R. , and S. , BiCMOS Analog Integrated Circuits for Embedded Spiking Neural Networks, Proeeding of XX Conference on Design of Circuits and Integrated Systems, pp.1-25, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00203934

R. Brette, M. Rudolph, T. Carnevale, M. Hines, D. Beeman et al., Simulation of networks of spiking neurons: A review of tools and strategies, Journal of Computational Neuroscience, vol.25, issue.54, pp.349-398, 2007.
DOI : 10.1007/s10827-007-0038-6
URL : https://hal.archives-ouvertes.fr/hal-00180662

L. Buhry, Estimation de paramètres de modèles de neurones biologiques sur une plate-forme de SNN (Spiking Neural Network) implantés "in silico, pp.1-4057, 2010.

L. Buhry, F. Grassia, A. Giremus, E. Grivel, S. Renaud et al., Automated Parameter Estimation of the Hodgkin-Huxley Model Using the Differential Evolution Algorithm: Application to Neuromimetic Analog Integrated Circuits, Neural Computation, vol.4, issue.10, pp.2599-2625, 2011.
DOI : 10.1023/A:1008880518515
URL : https://hal.archives-ouvertes.fr/hal-00625448

L. Buhry, S. Saïghi, A. Giremus, E. Grivel, R. et al., Parameter estimation of the Hodgkin-Huxley model using metaheuristics: Application to neuromimetic analog integrated circuits, 2008 IEEE Biomedical Circuits and Systems Conference, pp.173-176, 2008.
DOI : 10.1109/BIOCAS.2008.4696902
URL : https://hal.archives-ouvertes.fr/hal-00347187

A. Casti, A. Omurtag, A. Sornborger, E. Kaplan, B. Knight et al., A Population Study of Integrate-and-Fire-or-Burst Neurons, Neural Computation, vol.15, issue.5, pp.957-986, 2002.
DOI : 10.1017/S0952523800001784

P. S. Churchland, C. Koch, and T. J. Sejnowski, What is computational neuroscience?, Computational neuroscience, pp.46-55, 1993.

K. S. Cole, Dynamic electrical characteristics of the squid axon membrane, Arch. Sci. Physiol, vol.3, pp.253-258, 1949.

B. W. Connors and M. J. Gutnick, Intrinsic firing patterns of diverse neocortical neurons, Trends in Neurosciences, vol.13, issue.3, pp.99-104, 1990.
DOI : 10.1016/0166-2236(90)90185-D

D. C. Cooper, Introduction to neuroscience I. Donald C. Cooper Ph, 2011.

A. Daouzli, Systémes neuromorphiques: Etude et implantation de fonctions d'apprentissage et de plasticité, pp.1-3806, 2009.

E. De-la-peña and E. Geijo-barrientos, Laminar localization, morphology, and physiological properties of pyramidal neurons that have the low-threshold calcium current in the guinea-pig medial frontal cortex, The Journal of Neuroscience, issue.17, pp.165301-5311, 1996.

A. Destexhe, Simplified models of neocortical pyramidal cells preserving somatodendritic voltage attenuation, Neurocomputing, vol.38, issue.40, pp.167-173, 2001.
DOI : 10.1016/S0925-2312(01)00428-3
URL : https://hal.archives-ouvertes.fr/hal-00124664

A. Destexhe and J. Huguenard, Which formalism to use for modeling voltagedependent conductances?, Computational Neuroscience: Realistic Modeling for Experimentalists, pp.129-157, 2000.

A. Destexhe, Z. F. Mainen, and T. J. Sejnowski, An Efficient Method for Computing Synaptic Conductances Based on a Kinetic Model of Receptor Binding, Neural Computation, vol.30, issue.1, pp.14-18, 1994.
DOI : 10.1162/neco.1993.5.2.200

A. Destexhe, Z. F. Mainen, and T. J. Sejnowski, Kinetic models of synaptic transmission, Methods in Neuronal Modeling, vol.23, issue.83, pp.1-25, 1998.

A. Destexhe, M. Neubig, D. Ulrich, and J. Huguenard, Dendritic Low- Threshold Calcium Currents in Thalamic Relay Cells, The Journal of Neuroscience, vol.18, issue.10, pp.3574-3588, 1998.

A. Destexhe, M. Rudolph, and D. Pare, The high-conductance state of neocortical neurons in vivo, Nature Reviews Neuroscience, vol.4, issue.9, pp.739-751, 2003.
DOI : 10.1038/nrn1198
URL : https://hal.archives-ouvertes.fr/hal-00299172

E. Farquhar and P. Hasler, A bio-physically inspired silicon neuron, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.52, issue.3, pp.477-488, 2005.
DOI : 10.1109/TCSI.2004.842871

A. Feiner and A. J. Mcevoy, The Nernst Equation, Journal of Chemical Education, vol.71, issue.6, pp.71493-71497, 1994.
DOI : 10.1021/ed071p493

V. Feoktistov and S. Janaqi, Generalization of the strategies in differential evolution, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings., p.67, 2004.
DOI : 10.1109/IPDPS.2004.1303160

J. Fieres, J. Schemmel, M. , and K. , Training convolutional networks of threshold neurons suited for low-power hardware implementation, Proceedings of the International Joint Conference on Neural Networks, part of the IEEE World Congress on Computational Intelligence, pp.16-21, 2006.

R. Fitzhugh, Mathematical models of threshold phenomena in the nerve membrane, Conclusions and implications, pp.257-278, 1955.
DOI : 10.1007/BF02477753

R. Fitzhugh, Impulses and Physiological States in Theoretical Models of Nerve Membrane, Biophysical Journal, vol.1, issue.6, pp.445-466, 1961.
DOI : 10.1016/S0006-3495(61)86902-6

W. V. Geit, E. D. Schutter, and P. Achard, Automated neuron model optimization techniques: a review, Biological Cybernetics, vol.1, issue.4598, pp.241-251, 2008.
DOI : 10.1007/s00422-008-0257-6

W. Gerstner and W. M. Kistler, Spiking Neuron Models: Single Neurons, Populations , Plasticity, p.18, 2002.
DOI : 10.1017/CBO9780511815706

J. R. Gibson, M. Beierlein, and B. W. Connors, Two networks of electrically coupled inhibitory neurons in neocortex, Nature, vol.402, issue.71, pp.75-79, 1999.

B. P. Glackin, T. M. Mcginnity, L. P. Maguire, Q. Wu, and A. Belatreche, A Novel Approach for the Implementation of Large Scale Spiking Neural Networks on FPGA Hardware, Computational Intelligence and Bioinspired Systems, 8th International Work-Conference on Artificial Neural Networks, pp.552-563, 2005.
DOI : 10.1007/11494669_68

E. L. Graas, E. A. Brown, L. , and R. H. , An FPGA-Based Approach to High-Speed Simulation of Conductance-Based Neuron Models, Neuroinformatics, vol.2, issue.4, pp.417-435, 2004.
DOI : 10.1385/NI:2:4:417

F. Grassia, L. Buhry, T. Lévi, J. Tomas, A. Destexhe et al., Tunable neuromimetic integrated system for emulating cortical neuron models, Frontiers in Neuroscience, vol.5, issue.70, p.107, 2011.
DOI : 10.3389/fnins.2011.00134
URL : https://hal.archives-ouvertes.fr/hal-00684091

F. Grassia, T. Lévi, S. Saïghi, and T. Kohno, Bifurcation analysis in a silicon neuron, Artificial Life and Robotics, vol.23, issue.3, pp.53-58, 2012.
DOI : 10.1007/s10015-012-0016-6
URL : https://hal.archives-ouvertes.fr/hal-00775856

D. Hansel, G. Mato, and C. Meunier, Phase Dynamics for Weakly Coupled Hodgkin-Huxley Neurons, Europhysics Letters (EPL), vol.23, issue.5, pp.367-372, 1993.
DOI : 10.1209/0295-5075/23/5/011

P. E. Hasler, S. Koziol, E. Farquhar, and A. Basu, Transistor channel dendrites implementing HMM classifiers, 2007 IEEE International Symposium on Circuits and Systems, pp.3359-3362, 2007.
DOI : 10.1109/ISCAS.2007.378287

B. B. Hassard, Bifurcation of periodic solutions of the Hodgkin-Huxley model for the squid giant axon, Journal of Theoretical Biology, vol.71, issue.3, pp.401-420, 1978.
DOI : 10.1016/0022-5193(78)90168-6

B. D. Hassard, N. D. Kazarinoff, W. , and Y. , Theory and applications of Hopf bifurcation, p.45, 1981.

B. Hille, Ionic Channels of Excitable Membranes. Sinauer Associates, 2 sub edition, p.36, 1991.

J. L. Hindmarsh and R. M. Rose, A Model of Neuronal Bursting Using Three Coupled First Order Differential Equations, Proceedings of the Royal Society, pp.87-102, 1984.
DOI : 10.1098/rspb.1984.0024

M. L. Hines and N. T. Carnevale, The NEURON Simulation Environment, Neural Computation, vol.15, issue.6, pp.1179-1209, 1997.
DOI : 10.1088/0954-898X_5_1_002

A. L. Hodgkin, The local electric changes associated with repetitive action in a non-medullated axon, The Journal of Physiology, vol.107, issue.2, pp.165-181, 1948.
DOI : 10.1113/jphysiol.1948.sp004260

A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, pp.500-544, 1952.
DOI : 10.1113/jphysiol.1952.sp004764

G. Indiveri, E. Chicca, D. , and R. , A VLSI Array of Low-Power Spiking Neurons and Bistable Synapses With Spike-Timing Dependent Plasticity, IEEE Transactions on Neural Networks, vol.17, issue.1, pp.211-221, 2006.
DOI : 10.1109/TNN.2005.860850

G. Indiveri and S. Fusi, Spike-based learning in VLSI networks of integrate-andfire neurons, International Symposium on Circuits and Systems, pp.3371-3374, 2007.

E. M. 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. M. Izhikevich, Resonate-and-fire neurons, Neural Networks, vol.14, issue.6-7, pp.6-7883, 2001.
DOI : 10.1016/S0893-6080(01)00078-8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.2719

E. M. 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

E. M. Izhikevich, Which Model to Use for Cortical Spiking Neurons?, IEEE Transactions on Neural Networks, vol.15, issue.5, pp.1063-1070, 2004.
DOI : 10.1109/TNN.2004.832719

E. M. Izhikevich and G. M. Edelman, Large-scale model of mammalian thalamocortical systems, Proceedings of the National Academy of Sciences, vol.105, issue.9, pp.3593-3598, 2008.
DOI : 10.1073/pnas.0712231105

R. Jung, E. J. Brauer, and J. J. Abbas, Real-time interaction between a neuromorphic electronic circuit and the spinal cord, IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol.9, issue.3, pp.319-326, 2001.
DOI : 10.1109/7333.948461

E. R. Kandel, J. H. Schwartz, and T. M. Jessell, Principles of Neural Science, p.37, 2000.

D. Karaboga and S. Okdem, A simple and global optimization algorithm for engineering problems: Differential evolution algorithm 68 Conclusions and implications, Computer Journal of Turk Electronic Engineering, vol.12, issue.1, 2004.

N. Keren, N. Peled, and A. Korngreen, Constraining Compartmental Models Using Multiple Voltage Recordings and Genetic Algorithms, Journal of Neurophysiology, vol.94, issue.6, pp.3730-3742, 2005.
DOI : 10.1152/jn.00408.2005

R. Koene and M. Hasselmo, An Integrate-and-fire Model of Prefrontal Cortex Neuronal Activity during Performance of Goal-directed Decision Making, Cerebral Cortex, vol.15, issue.12, pp.1964-1981, 2005.
DOI : 10.1093/cercor/bhi072

L. Masson, G. , L. Masson, S. Moulins, and M. , From conductances to neural network properties: Analysis of simple circuits using the hybrid network method, Progress in Biophysics and Molecular Biology, vol.64, issue.2-3, pp.201-220, 1995.
DOI : 10.1016/S0079-6107(96)00004-1

L. Masson, G. Renaud-le-masson, S. Debay, D. Bal, and T. , Feedback inhibition controls spike transfer in hybrid thalamic circuits, Nature, vol.15, issue.6891, pp.854-858, 2002.
DOI : 10.1038/nature00825
URL : https://hal.archives-ouvertes.fr/hal-00124031

H. Lecar, Morris-Lecar model, Scholarpedia, vol.2, issue.10, pp.1333-1349, 2007.
DOI : 10.4249/scholarpedia.1333

D. R. Lester and S. Furber, Spinnaker: Distributed computer engineering for neuromorphics, Frontiers in Artificial Intelligence and Applications, vol.234, pp.324-331, 2011.

S. Liu and R. Douglas, Temporal Coding in a Silicon Network of Integrate-and-Fire Neurons, IEEE Transactions on Neural Networks, vol.15, issue.5, pp.1305-1314, 2004.
DOI : 10.1109/TNN.2004.832725

R. R. Llinás, The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function, Science, vol.242, issue.4886, pp.1654-1664, 1988.
DOI : 10.1126/science.3059497

M. Mahowald and R. Douglas, A silicon neuron, Nature, vol.354, issue.6354, pp.515-518, 1991.
DOI : 10.1038/354515a0

S. Millner, A. Hartel, J. Schemmel, M. , and K. , Towards biologically realistic multi-compartment neuron model emulation in analog vlsi, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learnin (ESANN), p.26, 2012.

J. Misra and I. Saha, Artificial neural networks in hardware: A survey of two decades of progress, Neurocomputing, vol.74, issue.1-3, pp.239-255, 2010.
DOI : 10.1016/j.neucom.2010.03.021

C. Morris and H. Lecar, Voltage oscillations in the barnacle giant muscle fiber, Biophysical Journal, vol.35, issue.1, pp.193-213, 1981.
DOI : 10.1016/S0006-3495(81)84782-0

J. Nagumo, S. Arimoto, Y. , and S. , An Active Pulse Transmission Line Simulating Nerve Axon, Proceedings of Institute of Radio Engineers, pp.2061-2070, 1962.
DOI : 10.1109/JRPROC.1962.288235

E. Neftci, E. Chicca, G. Indiveri, D. , and R. J. , A Systematic Method for Configuring VLSI Networks of Spiking Neurons, Neural Computation, vol.3, issue.10, pp.2457-2497, 2011.
DOI : 10.1162/neco.1989.1.3.334

M. Pospischil, M. Toledo-rodriguez, C. Monier, Z. Piwkowska, T. Bal et al., Minimal Hodgkin???Huxley type models for different classes of cortical and thalamic neurons, Biological Cybernetics, vol.17, issue.4-5, pp.427-441, 2008.
DOI : 10.1007/s00422-008-0263-8
URL : https://hal.archives-ouvertes.fr/hal-00377075

A. Rangan and D. Cai, Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks, Journal of Computational Neuroscience, vol.22, issue.1, pp.81-100, 2007.
DOI : 10.1007/s10827-006-8526-7

C. Rasche and R. Douglas, An improved silicon neuron, Analog Integrated Circuits and Signal Processing, vol.23, issue.3, pp.227-236, 2000.
DOI : 10.1023/A:1008357931826

S. Renaud, G. L. Masson, L. Alvado, S. Saïghi, T. et al., A neural simulation system based on biologically realistic electronic neurons, Information Sciences, vol.161, issue.1-2, pp.57-69, 2004.
DOI : 10.1016/j.ins.2003.03.007
URL : https://hal.archives-ouvertes.fr/hal-00203931

S. Renaud, J. Tomas, Y. Bornat, A. Daouzli, and S. Saïghi, Neuromimetic ICs with analog cores: an alternative for simulating spiking neural networks, 2007 IEEE International Symposium on Circuits and Systems, pp.3355-3358, 2007.
DOI : 10.1109/ISCAS.2007.378286
URL : https://hal.archives-ouvertes.fr/hal-00161313

S. Renaud, J. Tomas, N. Lewis, Y. Bornat, A. Daouzli et al., PAX: A mixed hardware/software simulation platform for spiking neural networks, Neural Networks, vol.23, issue.7, pp.905-916, 2010.
DOI : 10.1016/j.neunet.2010.02.006
URL : https://hal.archives-ouvertes.fr/hal-01179647

I. Reuveni, A. Friedman, Y. Amitai, and M. Gutnick, Stepwise repolarization from ca 2+ plateaus in neocortical pyramidal cells: evidence for nonhomogeneous distribution of hva ca 2+ channels in dendrites, The Journal of Neuroscience, issue.11, pp.134609-134630, 1993.

J. Rinzel and G. B. Ermentrout, Analysis of neural excitability and oscillations, Methods in neuronal modeling, p.42, 1989.

C. Rossant, D. F. Goodman, J. Platkiewicz, and R. Brette, Automatic fitting of spiking neuron models to electrophysiological recordings, Frontiers in Neuroinformatics, vol.4, issue.2, p.21, 2010.
DOI : 10.3389/neuro.11.002.2010

S. Saïghi, Circuits et systèmes de modélisation analogique de réseaux de neurones biologiques: application au développement d'outils pour les neurosciences computationnelles, pp.1-2891, 2004.

S. Saïghi, Y. Bornat, J. Tomas, G. L. Masson, R. et al., A Library of Analog Operators Based on the Hodgkin-Huxley Formalism for the Design of Tunable, Real-Time, Silicon Neurons, IEEE Transactions on Biomedical Circuits and Systems, vol.5, issue.1, pp.3-19, 2011.
DOI : 10.1109/TBCAS.2010.2078816

S. Saïghi, L. Buhry, Y. Bornat, G. N. Kaoua, J. Tomas et al., Adjusting the neurons models in neuromimetic ICs using the voltage-clamp technique, 2008 IEEE International Symposium on Circuits and Systems, pp.1564-1567, 2008.
DOI : 10.1109/ISCAS.2008.4541730

J. Schemmel, D. Bruderle, K. Meier, and B. Ostendorf, Modeling Synaptic Plasticity within Networks of Highly Accelerated I&F Neurons, 2007 IEEE International Symposium on Circuits and Systems, pp.3367-3370, 2007.
DOI : 10.1109/ISCAS.2007.378289

J. Schemmel, J. Fieres, M. , and K. , Wafer-scale integration of analog neural networks, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), pp.431-438, 2008.
DOI : 10.1109/IJCNN.2008.4633828

J. Shin and C. Koch, Dynamic range and sensitivity adaptation in a silicon spiking neuron, IEEE Transactions on Neural Networks, vol.10, issue.5, pp.1232-1238, 1999.
DOI : 10.1109/72.788662

M. F. Simoni, G. S. Cymbalyuk, M. E. Sorensen, R. L. Calabrese, and S. P. Deweerth, A Multiconductance Silicon Neuron With Biologically Matched Dynamics, IEEE Transactions on Biomedical Engineering, vol.51, issue.2, pp.51342-354, 2004.
DOI : 10.1109/TBME.2003.820390

P. Sjöström, E. Rancz, A. Roth, and M. Häusser, Dendritic Excitability and Synaptic Plasticity, Physiological Reviews, vol.88, issue.2, pp.769-840, 2008.
DOI : 10.1152/physrev.00016.2007

M. Sorensen, S. Deweerth, G. Cymbalyuk, and R. L. Calabrese, Using a Hybrid Neural System to Reveal Regulation of Neuronal Network Activity by an Intrinsic Current, Journal of Neuroscience, vol.24, issue.23, pp.5427-5438, 2004.
DOI : 10.1523/JNEUROSCI.4449-03.2004

R. Storn and K. Price, Differential evolution ? a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, vol.11, issue.4, pp.341-359, 1997.
DOI : 10.1023/A:1008202821328

R. D. Traub and R. Miles, Neuronal Networks of the Hippocampus, p.51, 1991.
DOI : 10.1017/CBO9780511895401

M. Vanier and J. Bower, A comparative survey of automated parameter-search methods for compartmental neural models, Journal of Computational Neuroscience, vol.7, issue.2, pp.149-171, 1999.
DOI : 10.1023/A:1008972005316

R. J. Vogelstein, U. Mallik, C. , and G. , Silicon spike-based synaptic array and address-event transceiver, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), pp.385-388, 2004.
DOI : 10.1109/ISCAS.2004.1329585
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.5901

W. M. Yamada, C. Koch, A. , and P. R. , Methods in neuronal modeling. chapter Multiple channels and calcium dynamics, pp.97-133, 1989.

T. Yu and G. Cauwenberghs, Analog VLSI Biophysical Neurons and Synapses With Programmable Membrane Channel Kinetics, IEEE Transactions on Biomedical Circuits and Systems, vol.4, issue.3, pp.139-148, 2010.
DOI : 10.1109/TBCAS.2010.2048566
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.423.6981