Connection profile robustness in a heterogeneous network of piecewise affine FitzHugh-Nagumo models

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 are given taking connection profile (coupling strength, delay length, subsystem heterogeneity) robustness into account. This result is accomplished through a linear multi-agent system perspective for a class of piecewise affine systems.