Broad edge of chaos in strongly heterogeneous Boolean networks

Details Broad edge of chaos in strongly heterogeneous Boolean networks Broad edge of chaos in strongly heterogeneous Boolean networks

2006-05-30

arxiv.org/abs/cond-mat/0605730v2

J. Phys. A: Math. Theor. 41 (2008) 415001

Physics

Condensed Matter

Statistical Mechanics

8 pages, 3 figures

Scientific paper

10.1088/1751-8113/41/41/415001

The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations. This turns out to behave in a universal way close to the phase boundary only for in-degree distributions with a finite second moment. In-degree distributions of the form $P_d(k)\sim k^{-\gamma}$ with $2<\gamma<3$, thus having a diverging second moment, lead to a slower increase of the Hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite $N$ with decreasing $\gamma$. We conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms.

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