Reaction-diffusion processes of three species on small-world networks

TL;DR

This paper investigates the decay dynamics of a three-species reaction-diffusion system on small-world networks, revealing power-law scaling of the global reaction rate and comparing results with regular networks.

Contribution

It introduces a numerical analysis of three-species reaction-diffusion processes on small-world networks, highlighting the impact of network randomness on decay behavior.

Findings

Global reaction rate follows power-law scaling with exponents 0.66 and -0.50 at different regimes.

Decay behavior differs between small-world and regular networks.

Crossover in reaction rate scaling observed with varying random link probability.

Abstract

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.