W. S. Mcculloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity, The Bulletin of Mathematical Biophysics, vol.5, issue.4, pp.115-133, 1943.
DOI : 10.1007/BF02478259

S. A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, Journal of Theoretical Biology, vol.22, issue.3, pp.437-467, 1969.
DOI : 10.1016/0022-5193(69)90015-0

R. Thomas, Boolean formalization of genetic control circuits, Journal of Theoretical Biology, vol.42, issue.3, pp.563-585, 1973.
DOI : 10.1016/0022-5193(73)90247-6

E. Goles and J. Olivos, Comportement periodique des fonctions a seuil binaires et applications, Discrete Applied Mathematics, vol.3, issue.2, pp.93-105, 1981.
DOI : 10.1016/0166-218X(81)90034-2

E. Goles, Fixed Point Behavior of Threshold Functions on a Finite Set, SIAM Journal on Algebraic Discrete Methods, vol.3, issue.4, pp.529-531, 1982.
DOI : 10.1137/0603054

F. Fogelman-soulie, E. Goles, and G. Weisbuch, Transient length in sequential iteration of threshold functions, Discrete Applied Mathematics, vol.6, issue.1, pp.95-98, 1983.
DOI : 10.1016/0166-218X(83)90105-1

J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proceedings of the National Academy of Sciences of the USA, pp.2554-2558, 1982.

J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons., Proceedings of the National Academy of Sciences of the USA, pp.3088-3092, 1984.
DOI : 10.1073/pnas.81.10.3088

E. H. Snoussi, Necessary Conditions for Multistationarity and Stable Periodicity, Journal of Biological Systems, vol.06, issue.01, pp.3-9, 1998.
DOI : 10.1142/S0218339098000042

J. Aracena, S. Ben-lamine, O. Mermet, O. Cohen, and J. Demongeot, Mathematical modeling in genetic networks: relationships between the genetic expression and both chromosomic breakage and positive circuits, IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), vol.33, issue.5, pp.33-825, 2003.
DOI : 10.1109/TSMCB.2003.816928

C. Soulé, Mathematical approaches to differentiation and gene regulation, Comptes Rendus Biologies, vol.329, issue.1, pp.13-20, 2006.
DOI : 10.1016/j.crvi.2005.10.002

M. Kaufman, C. Soulé, and R. Thomas, A new necessary condition on interaction graphs for multistationarity, Journal of Theoretical Biology, vol.248, issue.4, pp.675-685, 2007.
DOI : 10.1016/j.jtbi.2007.06.016

´. E. Remy, B. Mosse, C. Chaouiya, and D. Thieffry, A description of dynamical graphs associated to elementary regulatory circuits, Bioinformatics, vol.19, issue.Suppl 2, pp.172-178, 2003.
DOI : 10.1093/bioinformatics/btg1075

URL : https://hal.archives-ouvertes.fr/hal-01306959

´. E. Remy, P. Ruet, and D. Thieffry, Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework, Advances in Applied Mathematics, vol.41, issue.3, pp.335-350, 2008.
DOI : 10.1016/j.aam.2007.11.003

URL : https://hal.archives-ouvertes.fr/hal-00692086

A. Richard, Positive circuits and maximal number of fixed points in discrete dynamical systems, Discrete Applied Mathematics, vol.157, issue.15, pp.3281-3288, 2009.
DOI : 10.1016/j.dam.2009.06.017

A. Richard, Negative circuits and sustained oscillations in asynchronous automata networks, Advances in Applied Mathematics, vol.44, issue.4, pp.378-392, 2010.
DOI : 10.1016/j.aam.2009.11.011

R. Thomas, On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations, Series in Synergetics, vol.9, pp.180-193, 1981.
DOI : 10.1007/978-3-642-81703-8_24

S. A. Kauffman, The origins of order: self-organization and selection in evolution, 1993.

D. Hilbert, Mathematical problems, Bulletin of the American Mathematical Society, vol.8, issue.10, pp.437-479, 1902.
DOI : 10.1090/S0002-9904-1902-00923-3

J. Aracena, J. Demongeot, and E. Goles, Fixed points and maximal independent sets in AND???OR networks, Discrete Applied Mathematics, vol.138, issue.3, pp.277-288, 2004.
DOI : 10.1016/S0166-218X(03)00461-X

J. Aracena, J. Demongeot, and E. Goles, On limit cycles of monotone functions with symmetric connection graph, Theoretical Computer Science, vol.322, issue.2, pp.237-244, 2004.
DOI : 10.1016/j.tcs.2004.03.010

A. Richard and J. Comet, Necessary conditions for multistationarity in discrete dynamical systems, Discrete Applied Mathematics, vol.155, issue.18, pp.2403-2413, 2007.
DOI : 10.1016/j.dam.2007.04.019

URL : https://hal.archives-ouvertes.fr/hal-00342169

T. H. Müller, D. Swandulla, and H. U. Zeilhofer, Synaptic connectivity in cultured hypothalamic neuronal networks, Journal of Neurophysiology, vol.77, pp.3218-3225, 1997.

S. Grillner, The motor infrastructure: from ion channels to neuronal networks, Nature Reviews Neuroscience, vol.4, issue.7, pp.573-586, 2003.
DOI : 10.1038/nrn1137

L. Cangiano, Mechanisms of rhythm generation in the lamprey locomotor network, Karolinska Institute, 2004.

J. Demongeot, C. Jézéquel, and S. Sené, Boundary conditions and phase transitions in neural networks. Theoretical results, Neural Networks, vol.21, issue.7, pp.971-979, 2008.
DOI : 10.1016/j.neunet.2008.04.003

K. Ireland and M. Rosen, A classical introduction to modern number theory, 1990.

E. Goles, F. Fogelman-soulie, and G. Weisbuch, Specific roles of different Boolean mappings in random networks, Bulletin of Mathematical Biology, vol.44, pp.715-730, 1982.

N. J. Sloane, The on-line encyclopedia of integer sequences (OEIS)

J. Riordan, An introduction to combinatorial analysis, 1958.
DOI : 10.1063/1.3060724

H. Fredricksen and I. J. Kessler, Lexicographic compositions and deBruijn sequences, Journal of Combinatorial Theory, Series A, vol.22, issue.1, pp.17-30, 1977.
DOI : 10.1016/0097-3165(77)90059-0

URL : http://doi.org/10.1016/0097-3165(77)90059-0

F. Ruskey, Combinatorial generation. Preliminary working draft, 2003.

S. W. Golomb, Shift register sequences, 1967.
DOI : 10.1142/9361

N. J. Sloane, On single-deletion-correcting codes, Codes and Designs, de Gruyter, pp.273-291, 2002.

T. Vasiga and J. Shallit, On the iteration of certain quadratic maps over GF(p), Discrete Mathematics, vol.277, issue.1-3
DOI : 10.1016/S0012-365X(03)00158-4

F. G. Frobenius, Ueber die congruenz nach einem aus zwei endlichen gruppen gebildeten doppelmodul, J. reine angew. Math. (Crelles Journal), vol.101, pp.273-299, 1887.

E. Goles and M. Noual, Block-sequential update schedules and Boolean automata circuits, Discrete Mathematics and Theoretical Computer Science ? Proceedings of Automata' 2010, pp.0-41, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01185498

A. Elena, Robustesse des réseaux d'automates booléensbooléens`booléensà seuil aux modes d'itération. ApplicationàApplication`Applicationà la modélisation des réseaux de régulation génétique, 2009.

J. Demongeot, B. Amor, H. Elena, A. Gillois, P. Noual et al., Robustness in Regulatory Interaction Networks. A Generic Approach with Applications at Different Levels: Physiologic, Metabolic and Genetic, International Journal of Molecular Sciences, vol.10, issue.10, pp.4437-4473, 2009.
DOI : 10.3390/ijms10104437

URL : https://hal.archives-ouvertes.fr/hal-00644505

A. L. Barabási and Z. N. Oltvai, Network biology: understanding the cell's functional organization, Nature Reviews Genetics, vol.5, issue.2, pp.101-113, 2004.
DOI : 10.1038/nrg1272