Criticality in random threshold networks: annealed approximation and beyond

Random Threshold Networks with sparse. asymmetric connections show complex dynamical behavior similar to Random Boolean Networks. with a transition from ordered to chaotic dynamics at a critical average connectivity K-c. In this type of model-contrary to Boolean Networks-propagation of local perturbations (damage) depends on the in-degree of the sites. K-c is determined analytically. using an annealed approximation, and the results are con-firmed by numerical simulations. It is shown that the statistical distributions of damage spreading near the percolation transition obey power-laws, and dynamical correlations between active network clusters become maximal. We investigate the effect of local damage suppression at highly connected nodes for networks with scale-free in-degree distributions. Possible relations of our findings to proper-ties of real-world networks, like robustness and non-trivial degree-distributions, are discussed. (C) 2002 Elsevier Science B.V. All rights reserved.