Lyapunov Functions and Their USE in Automata Networks

  • F. Fogelman Soulie
Conference paper
Part of the NATO ASI Series book series (volume 20)


In this paper, we introduce the concept of Lyapunov function to study the dynamical behavior of automata networks. This notion, classical in continuous dynamical systems, has proved very useful for discrete systems as well.


Lyapunov Function Boolean Mapping Cellular Automaton Boolean Network Unique Fixed Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F. FOGELMAN SOULIE: Contributions à une Théorie du Calcul sur Réseaux. Thèse, Grenoble. 1985.Google Scholar
  2. [2]
    F. FOGELMAN SOULIE: Parallel and Sequential Computation on Boolean networks. Theoret. Comp. Sc., to appear.Google Scholar
  3. [3]
    F. FOGELMAN, E. GOLES, G. WEISBUCH: Transient Length in sequential Iterations of Threshold Functions. Disc. Appl. Math., 6, pp 95–98, 1983.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    F. FOGELMAN SOULIE, G. WEISBUCH:Random Iterations of Threshold Networks and Associative Memory. Submitted to SIAM J. on Computing. Google Scholar
  5. [5]
    E. GOLES CHACC: Positive Automata Networks. (this volume).Google Scholar
  6. [6]
    E. GOLES CHACC: Comportement Dynamique de Réseaux d’Automates. Thèse, Grenoble 1985.Google Scholar
  7. [7]
    E. GOLES CHACC, F. FOGELMAN SOULIE, D. PELLEGRIN: Decreasing Energy Functions as a Tool for Studying Threshold Networks. Disc. Appl. Math., to appear.Google Scholar
  8. [8]
    H. HARTMAN, G.Y. VICHNIAC: Inhomogeneous Cellular Automata, (this volume).Google Scholar
  9. [9]
    J.J. HOPFIELD: Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proc. Nat. Acad. Sc; USA, vol. 79, pp 2554–2558, 1982.CrossRefMathSciNetGoogle Scholar
  10. [10]
    S.A. KAUFFMAN: Behaviour of Randomly Constructed Genetic Nets. In “Towards a Theoretical Biology”. Ed. C.H. Waddington, Edinburgh Univ. Press, vol.3, pp 18–37, 1970.Google Scholar
  11. [11]
    S.A KAUFFMAN: Boolean Systems, Adaptive Automata, Evolution, (this volume).Google Scholar
  12. [12]
    D. PELLEGRIN: Dynamics of Random Boolean Networks, (this volume).Google Scholar
  13. [13]
    F. ROBERT: Basic Results for the Behaviour of Discrete Iterations, (this volume).Google Scholar
  14. [14]
    G. VICHNIAC: Cellular Automata Models of Disorder and Organization, (this volume).Google Scholar
  15. [15]
    G. WEISBUCH, D. D’HUMIERES: Determining the Dynamic Landscape of Hopfield Networks, (this volume).Google Scholar
  16. [16]
    G. WEISBUCH, F. FOGELMAN SOULIE: Scaling laws for the Attractors of Hopfield Networks. J. Physique Lett., 46, pp L623–L630, 1985.CrossRefGoogle Scholar
  17. [17]
    S WOLFRAM: Statistical Mechanics of Cellular Automata. Rev. of Modern Physics, 55–3, pp 601–645, 1983.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • F. Fogelman Soulie
    • 1
    • 2
  1. 1.LDRParisFrance
  2. 2.UER de Mathématiques, InformatiqueUniversité de Paris VParisFrance

Personalised recommendations