Critical Kauffman networks under deterministic asynchronous update

Abstract

We investigate the influence of a deterministic but non-synchronous update on random Boolean networks, with a focus on critical networks. Knowing that ‘relevant components’ determine the number and length of attractors, we focus on such relevant components and calculate how the length and number of attractors on these components are modified by delays at one or more nodes. The main findings are that attractors decrease in number when there are more delays and that periods may become very long when delay times are not integer multiples of the basic update step.