Lyapunov exponents in random Boolean networks

A new order parameter approximation to random boolean networks (RBN) is int roduced, 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 minimal perturbations. Finally, the Lyapunov exponents are obtained by m eans of different approximations: through distance method and a discrete va riant of the Wolf's method for continuous systems, (C) 2000 Elsevier Scienc e B.V. All rights reserved.