Effects of community structure on the dynamics of random threshold networks

Random threshold networks (RTNs) have been widely used as models of neural or genetic regulatory networks. Network topology plays a central role in the dynamics of these networks. Recently it has been shown that many social and biological networks are scale-free and also exhibit community structure, in which autonomous modules are wired together to perform relatively independent functions. In this study we use both synchronous and asynchronous models of RTNs to systematically investigate how community structure affects the dynamics of RTNs with scale-free topology. Extensive simulation experiments show that RTNs with high modularity have more attractors than those RTNs with low modularity, and RTNs with smaller communities tend to have more attractors. Damage resulting from perturbation of initial conditions spreads less effectively in RTNs with higher modularity and RTNs with smaller communities. In addition, RTNs with high modularity can coordinate their internal dynamics better than RTNs with low modularity under the synchronous update scheme, and it is the other way around under the asynchronous update. This study shows that community structure has a strong effect on the dynamics of RTNs.