Dynamical behavior and influence of stochastic noise on certain generalized Boolean networks

Gary L. Beck, Mihaela T Matache

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

This study considers a simple Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes. The network is analyzed when the connectivity k is fixed or variable. Making use of a Boolean rule that is a generalization of Rule 22 of elementary cellular automata, a generalized formula for providing the probability of finding a node in state 1 at time t is determined. We show typical behaviors of the iterations, and we study the dynamics of the network through Lyapunov exponents, bifurcation diagrams and fixed point analysis. We conclude that the network may exhibit stability or chaos, depending on the underlying parameters. In general high connectivity is associated with a convergence to zero of the probability of finding a node in state 1 at time t. We also study analytically and numerically the dynamics of the network under a stochastic noise procedure. We show that under a smaller probability of disturbing the nodes through the noise procedure the system tends to exhibit more nodes in the same state. For many parameter combinations there is no critical value of the noise parameter below which the network remains organized and above which it behaves randomly.

Original languageEnglish (US)
Pages (from-to)4947-4958
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Volume387
Issue number19-20
DOIs
StatePublished - Aug 1 2008

Fingerprint

Boolean Networks
Dynamical Behavior
Vertex of a graph
Connectivity
cellular automata
Bifurcation Diagram
iteration
Influence
chaos
Lyapunov Exponent
Cellular Automata
Critical value
diagrams
exponents
Chaos
Fixed point
Tend
Iteration
Zero

Keywords

  • Dynamical phase transition
  • Generalized elementary cellular automata rule 22
  • Random Boolean network
  • Stochastic noise
  • System dynamics
  • chaos

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Dynamical behavior and influence of stochastic noise on certain generalized Boolean networks. / Beck, Gary L.; Matache, Mihaela T.

In: Physica A: Statistical Mechanics and its Applications, Vol. 387, No. 19-20, 01.08.2008, p. 4947-4958.

Research output: Contribution to journalArticle

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