| Contents |
| We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity
means that some nodes in the network are massively connected, while the remaining nodes are only
poorly connected. We provide a probabilistic approach which enables us to describe the effective
dynamics of the massively connected nodes when taking a weak interaction limit. More precisely, we
show that for almost every random network and almost all initial conditions the high dimensional
network governing the dynamics of the massively connected nodes can be reduced to a few
macroscopic equations. Such reduction is intimately related to the ergodic properties of the expanding
maps. This reduction allows one to explore coherent properties of the network, such as hub
synchronization. |
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