PMID: 15244911Jul 13, 2004Paper

Random Boolean network model exhibiting deterministic chaos

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Mihaela Teodora Matache, Jack Heidel

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.

References

Nov 21, 1988·Journal of Theoretical Biology·D Stauffer
Jun 15, 1999·Theoretical Population Biology·L Stone, D Hart
Sep 16, 2000·Physical Review Letters·R Albert, A L Barabasi
May 12, 2001·Artificial Life·M A BedauT S Ray
Jun 5, 2003·Chaos·Jeffrey J. Fox, Colin C. Hill
Jun 5, 2003·Chaos·Xiaoyan Zhang, David F. Jarrett
Jul 11, 2003·Proceedings of the National Academy of Sciences of the United States of America·Maximino Aldana, Philippe Cluzel

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Citations

Oct 29, 2005·Chaos·Pauli RämöOlli Yli-Harja
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jan Nagler, Jens Christian Claussen
Mar 24, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Mihaela T Matache, Jack Heidel
Dec 13, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Juha KesseliOlli Yli-Harja

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