We study the order-chaos phase transition in random Boolean networks (RBNs), which have been used as models of gene regulatory networks. In particular we seek to characterize the phase diagram in information-theoretic terms, focusing on the effect of the control parameters (activity level and connectivity). Fisher information, which measures how much system dynamics can reveal about the control parameters, offers a natural interpretation of the phase diagram in RBNs. We report that this measure is maximized near the order-chaos phase transitions in RBNs, since this is the region where the system is most sensitive to its parameters. Furthermore, we use this study of RBNs to clarify the relationship between Shannon and Fisher information measures.

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CSIRO Information and Communications Technology Centre, PO Box 76, Epping, NSW 1710, Australia. E-mail: Rosalind.Wang@csiro.au (X.R.W.); Mikhail.Prokopenko@csiro.au (M.P.)

Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany. School of Information Technologies, The University of Sydney, NSW 2006, Australia. E-mail: lizier@mis.mpg.de