Dinâmica de redes booleanas aleatórias na presença de agente danificador

Abstract

We have performed computer simulations of Kauffman's automata on several graphs such as the regular square lattice and invasion percolation clusters in order to investigate phase transitions total entropy radial distributions of the mean total damage (dynamical exponent z) and propagation speeds of the damage when one adds a damaging agent in the system, nicknamed "strange man". Despite the increase in the damaging efficiency, we have not observed any appreciable change at the transition threshold to chaos neither for the short range nor for the small-word case on the square lattices when the strange man is added in comparison to when small initial damages are inserted in the system. The propagation speed of the damage cloud until touching the border of the system in both the short-range case as the small-word case obeys a power law with a critical exponent ɑ that strongly depends on the lattice. Particularly, we have checked the damage spreading when some connections are removed on the square lattice and when one considers sspecial invasion percolation clusters (high boundary-saturation clusters, HSBC). It is seen that the propagation speed in these systems is quite sensible to the degree of dilution on the square lattice and to the degree of boundary saturation on invasion percolation clusters. Finally, we expect that these and other more elaborated calculations will be helpful to understand more general problems concerning the propagation of simple defects in complex systems that are well described by cellular automata.