Measuring Mutual Information in Random Boolean Networks

Abstract

During the last few years an area of active research in the field of complex systems is that of their information storing and processing abilities. Common opinion has it that the most interesting beaviour of these systems is found ``at the edge of chaos'', which would seem to suggest that complex systems may have inherently non-trivial information proccesing abilities in the vicinity of sharp phase transitions. A comprenhensive, quantitative understanding of why this is the case is however still lacking. Indeed, even ``experimental'' (i.e., often numerical) evidence that this is so has been questioned for a number of systems. In this paper we will investigate, both numerically and analitically, the behavior of Random Boolean Networks (RBN's) as they undergo their order-disorder phase transition. We will use a simple mean field approximation to treat the problem, and without lack of generality we will concentrate on a particular value for the connectivity of the system. In spite of the simplicity of our arguments, we will be able to reproduce analitically the amount of mutual information contained in the system as measured from numerical simulations.