  Despite the incredible complexity of our brains' neural networks, theoretical
descriptions of neural dynamics have led to profound insights into possible
network states and dynamics. It remains challenging to develop theories that
apply to spiking networks and thus allow one to characterize the dynamic
properties of biologically more realistic networks. Here, we build on recent
work by van Meegen & Lindner who have shown that "rotator networks," while
considerably simpler than real spiking networks and therefore more amenable to
mathematical analysis, still allow to capture dynamical properties of networks
of spiking neurons. This framework can be easily extended to the case where
individual units receive uncorrelated stochastic input which can be interpreted
as intrinsic noise. However, the assumptions of the theory do not apply anymore
when the input received by the single rotators is strongly correlated among
units. As we show, in this case the network fluctuations become significantly
non-Gaussian, which calls for a reworking of the theory. Using a cumulant
expansion, we develop a self-consistent analytical theory that accounts for the
observed non-Gaussian statistics. Our theory provides a starting point for
further studies of more general network setups and information transmission
properties of these networks.
