Three-species reaction–diffusion processes on scale-free networks

We study the novel three-species reaction–diffusion processes of scale-free networks that are significantly different from numerical calculations manipulated on regular and small-world lattices. The inverse particle density for the three-species process scales according to the power-law with a scaling exponent α=1.5α=1.5 for γ>3γ>3. It is, however, found from numerical results that the inverse particle density scales in a different way depending on time tt when γ<3γ<3. In the early time regime, α≃1.5α≃1.5, but the inverse particle density increases exponentially over time. We also discuss the possible relationship with the dynamical properties of random walks. In particular, we measure the ratio between the number of inactive and active bonds which shows the segregation of the particles.