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Despite the incredible complexity of our brains' neural networks, theoreticaldescriptions of neural dynamics have led to profound insights into possiblenetwork states and dynamics. It remains challenging to develop theories thatapply to spiking networks and thus allow one to characterize the dynamicproperties of biologically more realistic networks. Here, we build on recentwork by van Meegen & Lindner who have shown that "rotator networks," whileconsiderably simpler than real spiking networks and therefore more amenable tomathematical analysis, still allow to capture dynamical properties of networksof spiking neurons. This framework can be easily extended to the case whereindividual units receive uncorrelated stochastic input which can be interpretedas intrinsic noise. However, the assumptions of the theory do not apply anymorewhen the input received by the single rotators is strongly correlated amongunits. As we show, in this case the network fluctuations become significantlynon-Gaussian, which calls for a reworking of the theory. Using a cumulantexpansion, we develop a self-consistent analytical theory that accounts for theobserved non-Gaussian statistics. Our theory provides a starting point forfurther studies of more general network setups and information transmissionproperties of these networks.

A self-consistent analytical theory for rotator networks under stochastic forcing: effects of intrinsic noise and common input