Searching for Rhythms in Asynchronous Random Boolean Networks

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4 Author(s)

Many interesting properties of Boolean networks, cellular automata, and other models of complex systems rely heavily on the use of synchronous updating of the individual elements. This has motivated some researchers to claim that, if the natural systems being modelled lack any clear evidence of synchronously driven elements, then asynchronous rules should be used by default. Given that standard asynchronous updating precludes the possibility of strictly cyclic attractors, does this mean that asynchronous Boolean networks, cellular automata, etc., are inherently bad choices at the time of modelling rhythmic phenomena? In this paper we focus on this subsidiary issue for the case of Asynchronous Random Boolean Networks (ARBNs). We find that it is rather simple to define measures of pseudo-periodicity by using correlations between states and sufficiently relaxed statistical constraints. These measures can be used to guide an evolutionary search process to find appropriate examples. Success in this search for a number of cases, and subsequent statistical studies lead to the conclusion that ARBNs can indeed be used as models of coordinated rhythmic phenomena, which may be stronger precisely because of their built-in asynchrony. The methodology is flexible, and allows for more demanding statistical conditions for defining pseudo-periodicity, and constraining the evolutionary search