Phase transition in NK-Kauffman networks and its correction for Boolean irreducibility
Por:
Zertuche, F
Publicada:
1 may 2014
Resumen:
In a series of articles published in 1986, Derrida and his colleagues studied two mean field treatments (the quenched and the annealed) for NK-Kauffman networks. Their main results lead to a phase transition curve Kc2pc(1-pc)=1 (0<pc<1) for the critical average connectivity Kc in terms of the bias pc of extracting a "1" for the output of the automata. Values of K bigger than Kc correspond to the so-called chaotic phase, while K<Kc, to an ordered phase. In Zertuche (2009), a new classification for the Boolean functions, called Boolean irreducibility, permitted the study of new phenomena of NK-Kauffman networks. In the present work we study once again the mean field treatment for NK-Kauffman networks, correcting it for Boolean irreducibility. A shifted phase transition curve is found. In particular, for pc=1/2 the predicted value Kc=2 by Derrida et al. changes to Kc=2.62140224613. We support our results with numerical simulations. © 2014 Elsevier B.V. All rights reserved.
Filiaciones:
Zertuche, F:
Univ Nacl Autonoma Mexico, Unidad Cuernavaca, Inst Matemat, Cuernavaca 62251, Morelos, Mexico
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