W. S. Mcculloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity, Journal of Mathematical Biology, vol.5, pp.115-133, 1943.

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. 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. Rémy, 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

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. 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. 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

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, 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

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

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

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

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

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

T. H. Müller, D. Swandulla, and H. U. Zeilhofer, Synaptic connectivity in cultured hypothalamic neuronal networks, Journal of Neurophysiology, vol.77, issue.6, pp.3218-3225, 1997.

E. Goles, F. Fogelman-soulie, and G. Weisbuch, Specific roles of different boolean mappings in random networks, Bulletin of Mathematical Biology, vol.44, issue.5, pp.715-730, 1982.

T. M. Apostol, Introduction to analytic number theory, 1976.

J. Aracena, Discrete mathematics models associated to biological systems. Application to the genetic regulatory networks, 2001.

N. J. Sloane, The On-Line Encyclopedia of Integer Sequences, 2008.
DOI : 10.1007/978-3-540-73086-6_12

F. Ruskey, Information on necklaces, unlabelled necklaces, Lyndon words

S. W. Golomb, Shift register sequences, 1981.
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

W. Burnside, Theory of groups of finite order, 1897.

F. G. Frobenius, Ueber die Congruenz nach einem aus zwei endlichen Gruppen gebildeten Doppelmodul, Crelle CI, p.288, 1887.

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