Dynamical Coarse Graining of Large Scale-Free Boolean networks

Details Dynamical Coarse Graining of Large Scale-Free Boolean networks Dynamical Coarse Graining of Large Scale-Free Boolean networks

2006-03-07

arxiv.org/abs/cond-mat/0603167v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 6 figures

Scientific paper

We present a renormalization-grouplike method performed in the state space for detecting the dynamical behaviors of large scale-free Boolean networks, especially for the chaotic regime as well as the edge of chaos. Numerical simulations with different coarse-graining level show that the state space networks of scale-free Boolean networks follow universal power-law distributions of in and out strength, in and out degree, as well as weight. These interesting results indicate scale-free Boolean networks still possess self-organized mechanism near the edge of chaos in the chaotic regime. The number of state nodes as a function of biased parameter for distinct coarse-graining level also demonstrates that the power-law behaviors are not the artifact of coarse-graining procedure. Our work may also shed some light on the investigation of brain dynamics.

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