### Abstract

This paper considers a simple Boolean network with N nodes, each node's state at time t 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 t, 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 language | English (US) |
---|---|

Pages (from-to) | 56214 |

Number of pages | 1 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 69 |

Issue number | 5 |

State | Published - May 1 2004 |

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### ASJC Scopus subject areas

- Medicine(all)

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*69*(5), 56214.

**Random Boolean network model exhibiting deterministic chaos.** / Matache, Mihaela T; Heidel, Jack.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 69, no. 5, pp. 56214.

}

TY - JOUR

T1 - Random Boolean network model exhibiting deterministic chaos

AU - Matache, Mihaela T

AU - Heidel, Jack

PY - 2004/5/1

Y1 - 2004/5/1

N2 - This paper considers a simple Boolean network with N nodes, each node's state at time t 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 t, 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.

AB - This paper considers a simple Boolean network with N nodes, each node's state at time t 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 t, 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.

UR - http://www.scopus.com/inward/record.url?scp=84965087951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84965087951&partnerID=8YFLogxK

M3 - Article

VL - 69

SP - 56214

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 5

ER -