Fig. 5.

Phase space for signaling networks with mixing of Boolean rules. We systematically calculate the exponent α, by characterizing the correlations in the dynamics, for systems composed of units operating according to rule 232 but with some fixed fraction of units operating according to a randomly selected symmetric Boolean rule. Each value is an average over five independent runs. (a) One-sixteenth of the units operating according to a randomly selected rule. (b) One-eighth of the units operating according to a randomly selected rule. (c) One-fourth of the units operating according to a randomly selected rule. (d) One-half of the units operating according to a randomly selected rule. These figures suggest that the presence of random Boolean functions leads to a decrease in the richness of the phase space of the systems. Specifically, if more than one-fourth of all of the units operate according to randomly selected Boolean functions, then the phase space displays mostly white-noise dynamics.