FitzHugh-Nagumo is one of the best known nonlinear neuronal models in mathematical physiology. In particular, spatio-temporal forms of this model have been used for modeling oscillatory behavior in living organisms such as the behavior of cardiac pacemaker cells. In this paper, we investigate the stability of their spatially discretized form, that is, diffusively coupled large-scale networks of piecewisely affine approximated FitzHugh-Nagumo models. Scalable criteria for ultimate boundedness ...