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Structural control of reaction-diffusion networks.

Recent studies revealed that reaction-diffusion (RD) dynamics can be significantly influenced by the structure of the underlying network. In this paper, a framework is established to study a closely related problem, i.e., to control the proportion of active particles in an RD process by adjusting the structure of the underlying diffusion network. Both distributed and centralized rewiring and reweighting control schemes are proposed for unweighted and weighted networks, respectively. Simulations show that the proportion of active particles can indeed be controlled to a certain extent even when the distributed control mechanism is totally random, while quite high precision can be achieved by centralized control schemes. More interestingly, it is found that the reactants in heterogeneous networks have wider controllable ranges than those in homogeneous networks with similar numbers of nodes and links, if only the weights of links are changed with a fixed bound. Therefore, it is believed that heterogeneous networks fit the changeable environment better, which provides another explanation for some common observations on many heterogeneous real-world networks.