Dynamical behavior of Kauffman networks with and-or gates

Eric Goles, Gonzalo Hernandez

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We study the parallel dynamics of a class of Kauffman boolean nets such that each vertex has a binary state machine {AND, OR} as local transition function. We have called this class of nets AON. In a finite, connected and undirected graph, the transient length, attractors and its basins of attraction are completely determined in the case of only OR (AND) functions in the net. For finite, connected and undirected AON, an exact linear bound is given for the transient time using a Lyapunov functional. Also, a necessary and sufficient condition is given for the diffusion problem of spreading a one all over the net, which generalizes the primitivity notion on graphs. This condition also characterizes its architecture. For finite, strongly connected and directed AON a non-polynomial time bound is given for the transient time and for the period on planar graphs, together with an example where this transient time and period are attained. Furthermore, on infinite but finite connected, directed and non planar AON we simulate an universal two-register machine, which allows us to exhibit universal computing capabilities.

Original languageEnglish
Pages (from-to)151-175
Number of pages25
JournalJournal of Biological Systems
Volume8
Issue number2
DOIs
StatePublished - Jun 2000
Externally publishedYes

Keywords

  • Boolean nets periods
  • Connected and primitive graphs
  • Discrete dynamical systems
  • Lyapunov functionals
  • Transient times

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