We consider oscillatory systems of interacting Hawkes processes introduced inDitlevsen and Loecherbach (2017) to model multi-class systems of interactingneurons together with the diffusion approximations of their intensityprocesses. This diffusion, which incorporates the memory terms defining thedynamics of the Hawkes process, is hypo-elliptic. It is given by a highdimensional chain of differential equations driven by $2-$dimensional Brownianmotion. We study the large-population-, i.e., small noise-limit of itsinvariant measure for which we establish a large deviation result in the spiritof Freidlin and Wentzell.
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