Random Boolean network model exhibiting deterministic chaos

Mihaela T. Matache, Jack Heidel

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

This paper considers a simple Boolean network with [Formula presented] nodes, each node’s state at time [Formula presented] being determined by a certain number of parent nodes, which may vary from one node to another. This is an extension of a model studied by Andrecut and Ali [Int. J. Mod. Phys. B 15 17 2001], who consider the same number of parents for all nodes. We make use of the same Boolean rule as Andrecut and Ali, provide a generalization of the formula for the probability of finding a node in state 1 at a time [Formula presented], and use simulation methods to generate consecutive states of the network for both the real system and the model. The results match well. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the route to chaos is due to a cascade of period-doubling bifurcations which turn into reversed (period-halving) bifurcations for certain combinations of parameter values.

Original languageEnglish (US)
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume69
Issue number5
DOIs
StatePublished - Jan 1 2004

Fingerprint

Random Boolean Networks
Deterministic Chaos
Boolean Model
Network Model
chaos
Vertex of a graph
period doubling
Boolean Networks
cascades
Period-doubling Bifurcation
diagrams
routes
Bifurcation Diagram
orbits
Simulation Methods
Cascade
Consecutive
sensitivity
Chaos
Bifurcation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

Cite this

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