  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.
