Dynamics of Critical Kauffman Networks under Asynchronous Stochastic Update

We show that the mean number of attractors in a critical Boolean network under asynchronous stochastic update grows like a power law and that the mean size of the attractors increases as a stretched exponential with the system size. This is in strong contrast to the synchronous case, where the number of attractors grows faster than any power law.

Figure 1

A possible sequence of configurations of a loop with a cross-link showing how multiple domain walls are generated. The coupling function of the node ○ with two inputs is such that only two dark inputs lead to light output, all other combination give black output. After (e) the procedure described by (a) to (d) is repeated to obtain (f) and similarly for (g), (h) and (i).