  We study the decay process for the reaction-diffusion process of three
species on the small-world network. The decay process is manipulated from the
deterministic rate equation of three species in the reaction-diffusion system.
The particle density and the global reaction rate on a two dimensional
small-world network adding new random links is discussed numerically, and the
global reaction rate before and after the crossover is also found by means of
the Monte Carlo simulation. The time-dependent global reaction rate scales as a
power law with the scaling exponent 0.66 at early time regime while it scales
with -0.50 at long time regime, in all four cases of the added probability
$p=0.2-0.8$. Especially, our result presented is compared with the numerical
calculation of regular networks.
