Coupled dynamics on networks

We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the network. For small coupling strengths, nodes show turbulent behavior but form synchronized clusters as coupling increases. When nodes show synchronized behavior, we observe two interesting phenomena. Firstly, there are some nodes of the floating type that show intermittent behavior between getting attached to some clusters and evolving independently. Secondly, we identify two different ways of cluster formation, namely self-organized clusters which have mostly intra-cluster couplings and driven clusters which have mostly inter-cluster couplings.