Morphological property of innovation propagation on complex networks

 

SOON-HYUNG YOOK

KYUNG HEE UNIVERSITY

 

We study the dynamical properties of the propagation of innovation on complex networks. In order to investigate the diversity of technological level, we study the scaling property of width, $W(N,t)$, which represents the mean-square-root of the technological level of agents. Here, $N$ is the total number of agents. From the numerical simulations, we find that the steady-state value of $W(N,t)$, $W_{sat}(N)$, scales as$W_{sat}(N)\sim N^{-1/2}$ when the system is in a {\it flat ordered phase} for $d\ge 2$. In the {\it flat ordered phase}, most of the agents have the same technological level. On the other hand when the system is in a {\it smooth disordered phase}, the value of $W_{sat}(N)$ does not depend on $N$. For the comparison, we also measure $W(N,t)$ on regular lattices. The results provides an evidence that the upper critical dimension for the roughening transition of the propagation of innovation is $d_u=2$.