Reaction-Diffusion Processes on Networks

We study the novel reaction-diffusion process of three-species on scale-free networks, which is significantly different from the numerical calculation manipulated on regular and small-world lattices. The inverse particle density for three-species process scales as the power-law behavior with $\alpha=1.5$ for $\gamma>3 $. However we find that the inverse particle density scales in a different way depending on time $t$ when $\gamma<3$. In the early time regime, $\alpha\simeq 1.5$ but the inverse particle density increases exponentially as time increases. We also discuss the possible relationship to the dynamical properties of random walks. Particularly, we measure the ratio between the number of inactive and active bonds which shows the segregation of the particles.