In this thesis we study the dynamics of expanding circle maps on networked systems. In particular, we focus our attention on those networks in which the underlying structure is given by a heterogeneous graph, that is, few nodes in the networks are massively connected, while the number of connections for the remaining nodes is significantly smaller.
We show that for the massively connected nodes, the deviation between a mean field reduction and the true dynamics is a random fluctuation that converges to a normal distribution in the large system size limit.