Synchronism vs Asynchronism in Boolean networks

Abstract

We show that synchronism can significantly impact on network behaviours, in particular by filtering unstable attractors induced by a constraint of asynchronism. We investigate and classify the different possible impacts that an addition of synchronism may have on the behaviour of a Boolean automata network. We show how these relate to some strong specific structural properties, thus supporting the idea that for most networks, synchronism only shortcuts asynchronous trajectories. We end with a discussion on the close relation that apparently exists between sensitivity to synchronism and non-monotony.