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Phase Transition in NK-Kauffman Networks and its Correction for Boolean Irreducibility
In a series of articles published in 1986 Derrida, and his colleagues studied
two mean field treatments (the quenched and the annealed) for
\textit{NK}-Kauffman Networks. Their main results lead to a phase transition
curve () for the
critical average connectivity in terms of the bias of
extracting a "" for the output of the automata. Values of bigger than
correspond to the so-called chaotic phase; while , to an
ordered phase. In~[F. Zertuche, {\it On the robustness of NK-Kauffman networks
against changes in their connections and Boolean functions}. J.~Math.~Phys.
{\bf 50} (2009) 043513], a new classification for the Boolean functions, called
{\it Boolean irreducibility} permitted the study of new phenomena of
\textit{NK}-Kauffman Networks. In the present work we study, once again the
mean field treatment for \textit{NK}-Kauffman Networks, correcting it for {\it
Boolean irreducibility}. A shifted phase transition curve is found. In
particular, for the predicted value by Derrida {\it
et al.} changes to We support our results with
numerical simulations.Comment: 23 pages, 7 Figures on request. Published in Physica D: Nonlinear
Phenomena: Vol.275 (2014) 35-4
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