Order Parameters, Lyapunov Exponents, and Control in Random Boolean Networks

A new order parameter approximation to Random Boolean Networks (RBN) is introduced, based on the concept of Boolean derivative. A statistical argument involving an annealed approximation is used, allowing to measure the order parameter in terms of the statistical properties of a random matrix. Using the same formalism, a Lyapunov exponent is calculated, allowing to provide the onset of damage spreading through the network and how sensitive it is to single flips. Finally, these measures are used in order to estimate the critical boundaries for chaos control in RBN.