Reaction diffusion processes on random and scale-free networks

TL;DR

This paper investigates reaction-diffusion processes on various network types, revealing how network topology influences pattern formation, with notable differences observed between regular, random, and scale-free networks.

Contribution

It introduces a study of the Gierer-Meinhardt model on different networks, highlighting the impact of network structure on Turing pattern formation.

Findings

Pattern formation varies significantly across network types.

Random and scale-free networks exhibit distinct pattern behaviors from regular networks.

Small world properties influence the emergence and nature of stationary patterns.

Abstract

We study the discrete Gierer-Meinhardt model of reaction-diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain parameter regions. Some general features of the patterns are studied through numerical simulation. The results for the random and scale-free networks show a marked difference from those in the case of the regular network. The difference may be ascribed to the small world character of the first two types of networks.