Abstract
There has been an improved effort for about 20 years in studying the dynamical behaviour of discrete, iterative systems. The reason for this is probably that different (but conceptually similar) discrete models are presently of interest in various domains of science, such as: Physics (spin glass problems, see (10), (12), (14), for example), Chemistry (diffusion reactions (9)), Biomathematics (neural networks, genetic nets, (10), (11), (14), (18), (20)), Computer Science (pattern recognition, associative memories (7), (10), cellular automata (1), (2), (9), (19), (21), (22), (23), cellular arrays for systolic computation in V.L.S.I. systems (13), (15), (17), (19) and so on: see especially (4), (5), (6)).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A.W. BURKS: Essays on cellular Automata., University of Illinois Press (1970).
E.F. CODD: Cellular Automata., Academic Press (1968).
M. COSNARD, E. GOLES: Dynamique d’un automate à mémoire modélisant le fonctionnement d’un neurone., C.R.A.S., t. 299, I N° 10, (1984). (see also the papers by M. Cosnard and E. Goles in the present volume)
M. COSNARD, J. DEMONGEOT, A. LEBRETON, Editors: Rythms in biology and other fields of Applications. Springer Verlag, Lecture notes in Mathematics n°49 (1983).
J. DELLA DORA, J. DEMONGEOT, B. LACOLLE, Editors: Numerical methods in study of critical phenomena., Springer Verlag (1981).
J. DEMONGEOT, E. GOLES, M. TCHUENTE, Editors: Dynamic behaviour of automata networks, Academic Press (1984).
F. FOGELMAN: Contributions à une théorie du calcul sur réseaux. Thesis, Grenoble 1985. (see also the paper by F. Fogelman in the present volume.)
E. GOLES: Comportement dynamique de réseaux d’automates. Thesis, Grenoble 1985. (see also the paper by E. Goles in the present volume.)
J.M. GREENBERG, B.D. HASSARD, S.P. HASTINGS: Pattern formation and periodic structures in systems modelled by reaction diffusion equations. Bull. Am. Math. Soc. 84. 6, p. 1296–1327 (1978).
J. J. HOPFIELD: Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sc. U.S.A. (79), p. 2554–2558 (1982).
S. KAUFFMAN: Behaviour of randomly constructed genetic nets. in Towards a theoretical biology, Vol3, Edinburgh University Press, p. 18–46 (1970).
S. KIRKPATRICK: Models of disordered materials. In Ill condensed matter, Les Houches, North Holland (1979).
C.A. MEAD, M.A. CONWAY: Introduction to V.L.S.I systems Addison Wesley, (1980).
P. PERETTO: Collective properties of neural networks; A statistical physics approach. (to appear in Biological Cybernetics.)
P. QUINTON: The systematic design of systolic arrays. (to appear).
F. ROBERT: Discrete iterations Springer Verlag (to appear).
Y. ROBERT: Thesis, Grenoble (to appear).
R. SHINGAI: Maximum period of 2-dimensional uniform neural networks Inf and Control (11), 324–341, (1979).
M. TCHUENTE: Contribution à l’étude des méthodes de calcul pour des systèmes de type coopératif, Thesis, Grenoble (1982). (see also the paper by M. Tchuente in the present volume.)
R. THOMAS: Kinetic Logic, Lecture Notes in biomathematics, Vol 29, Springer Verlag (1979).
J. VON NEUMANN: Theory of self reproducing automata., A.W. Burks Editor; University of Illinois Press (1966).
S. WOLFRAM (Editor): Cellular automata. Los Alamos Science (1984).
S. WOLFRAM: Statistical mechanics of cellular automata. Rev. Mod. phys. 55, n° 3, 601–642 (1983).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Robert, F. (1986). Basic Results for the Behaviour of Discrete Iterations. In: Bienenstock, E., Soulié, F.F., Weisbuch, G. (eds) Disordered Systems and Biological Organization. NATO ASI Series, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82657-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-82657-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-82659-7
Online ISBN: 978-3-642-82657-3
eBook Packages: Springer Book Archive