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I need some direction on the topic of Random boolean networks (NK-boolean networks or Kauffman automata). I know some of the results like if K=1 the systems settles down to fixed points, if K=2 it oscillates with some period or settles to fixed point, if K>2 it goes to chaos regime. But I would like to see the proofs for those and wanted to find the number of attractors and size of basins.

Can some one give me some hints or at least papers, links and books etc related to these.

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Here is a PhD thesis on exactly this topic. That should include enough further references for you: http://tuprints.ulb.tu-darmstadt.de/1905/2/FlorianGreil_PhDThesis_TuDarmstadt.pdf

In general, all results are average results. That is, you may have a network with k=2 that behaves very chaotic (long attractors etc.) and you may have a network with k>>2 with ordered dynamics.

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  • $\begingroup$ Let me see that. Seems to be very good document. $\endgroup$ – dexterdev Feb 16 '15 at 7:56

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