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Random Boolean network model exhibiting deterministic chaos.

Mihaela T Matache1, Jack Heidel

  • 1Department of Mathematics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0243, USA. dmatache@mail.unomaha.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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This study extends Boolean networks by allowing variable parent nodes per node. Simulations confirm the model

Area of Science:

  • Computational Biology
  • Complex Systems
  • Network Science

Background:

  • Boolean networks are used to model biological systems.
  • Previous models assumed a fixed number of parent nodes for all nodes.
  • This study extends prior work by allowing variable parent nodes.

Purpose of the Study:

  • To generalize a Boolean network model with variable parent nodes.
  • To analyze the dynamics and route to chaos in these networks.
  • To validate the model through simulations and comparison with existing work.

Main Methods:

  • Generalization of the probability formula for node states.
  • Network state simulation for real and model systems.
  • Analysis of orbit sensitivity, bifurcation diagrams, and fixed points.

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Main Results:

  • Simulations show good agreement between the model and real systems.
  • The model exhibits a route to chaos via period-doubling bifurcations.
  • Parameter combinations can lead to reversed (period-halving) bifurcations.

Conclusions:

  • The generalized Boolean network model accurately represents system dynamics.
  • The study elucidates the mechanisms driving the transition to chaos.
  • Findings provide insights into complex system behavior and stability.