Dynamics of Scale Free Random Threshold Network

We study the dynamics of Random Threshold Network (RTN) on scale free networks, with asymmetric links, some interaction rules where propagation of local perturbations depends on in-degree $k$ of the nodes. We find that there is no phase transition with respect to average connectivty independently of network topology for the case temperature T=0, threshold $h=0$ and the probability distribution of indegree $P(k)$ satisfies $P(0)=D=0$. We have investigated the emergence of phase transition involving three parameters, i.e. $T,h$ and $D$. RTN can be continuously connected to Random Boolean Network (RBN) in $T\to \infty$, and we find moderate thermal noise extends the regime of ordered dynamics, compared to RTN in T=0 regime and RBN. Furthermore, we discuss the dynamic properties from another point of view, dynamical mean field reaction rate equation.