Microscopic self-organization in networks

We report our numerical studies on microscopic self-organization of a reaction system in three types of differently connected networks: a regular network, a small-world network, and a random network. Our simulation results show that the topology of the network has an important effect on the communication among reaction molecules, and plays an important role in microscopic self-organization. The correlation length among reacting molecules in a random or a small-world network is much shorter compared with that in a regular one. As a result, it is much easier to obtain microscopic self-organization in a small-world or a random network. We also observed a phase transition from a stochastic state to a synchronized state when we increased the randomness of a small-world network.