%0 Journal Article
%T Broad edge of chaos in strongly heterogeneous Boolean networks
%A Deok-Sun Lee
%A Heiko Rieger
%J Mathematics
%D 2006
%I arXiv
%R 10.1088/1751-8113/41/41/415001
%X 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.
%U http://arxiv.org/abs/cond-mat/0605730v2