A Scale-free Network with Boolean Dynamics as a Function of Connectivity

Abstract

In this work we analyze scale-free networks with different power law spectra $N(k)\sim k^{-\gamma }$ under a boolean dynamic, where the boolean rule that each node obeys is a function of its connectivity $k$. This is done by using only two logical functions (AND and XOR) which are controlled by a parameter $q$. Using damage spreading technique we show that the Hamming distance and the number of 1's exhibit power law behavior as a function of $q$. The exponents appearing in the power laws depend on the value of $\gamma$.

8 pages, 7 Postscript; to appear in Phys. Rev. E