Emergence of heterogeneous structures in chemical reaction-diffusion networks

This paper suggests that reaction-diffusion processes, rather than pure topological rules, are responsible for the emergence of heterogeneous structures of complex chemical reaction networks. In such a network, chemical substances react in each node and diffuse between connected nodes. At the same time, each node is able to sense the difference between its own state and the environmental conditions and can rearrange its neighbors via a local rewiring process so as to eliminate the sensed difference. Then, the network, even originally homogeneous, will develop a heterogeneous structure under certain environmental conditions. Such a resultant heterogeneous network may be disassortative, highly clustering, and small world as well. This implies that the reaction-diffusion equilibrium can be statistically controlled by slightly changing the structure of the underlying network. This structure-control mechanism may be especially useful in the situations where some other macroscopic measurements, such as temperature and pressure, are not allowed to be changed through the process.