The formation of the frozen core in critical Boolean networks

Details The formation of the frozen core in critical Boolean networks The formation of the frozen core in critical Boolean networks

Feb 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012njph...14b3051m&link_type=abstract

New Journal of Physics, Volume 14, Issue 2, pp. 023051 (2012).

Physics

Scientific paper

We investigate numerically and analytically the formation of the frozen core in critical random Boolean networks with biased functions. We demonstrate that a previously used efficient algorithm for obtaining the frozen core, which starts from the nodes with constant functions, fails when the number of inputs per node k exceeds 4. We present computer simulation data for the process of formation of the frozen core and its robustness and show that several important features of the data can be derived using a mean-field calculation. Our results show that the dynamics of the formation of the frozen core for k > 4 are very similar to those for the case of k ⩽ 4. As in the case of k ⩽ 4, most nodes also always become frozen on the same value for k > 4, with the possible exception of very special configurations that are not visible in either computer simulations that start from random initial states or in mean-field theory, which evaluates what happens typically.

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