Nonmonotonic reorganization of excitation and relaxation in multidimensional excitable media

We analyze excitation and relaxation dynamics in a two-dimensional heterogeneous excitable medium described by a smoothly regularized three-variable Fenton-Karma model. To relate spatial heterogeneity to a global observable, we examine the dipole response together with the evolution of two activation-threshold manifolds associated with distinct regimes of the excitation-relaxation dynamics of the model. We show that increasing diffusion contrast does not produce a monotonic change in the global excitation-relaxation organization. For weak contrast, excitation remains globally connected despite deformation of the excitation pattern. For intermediate contrast, the system fails to establish a globally connected excited state outside the heterogeneous region, leading to the disappearance of the characteristic negative T-wave-like minimum in the dipole signal. However, a further increase in diffusion contrast restores global connectivity despite the persistence of a trapped low-potential region within the heterogeneity. These results demonstrate that localized heterogeneity can induce a nonmonotonic reorganization of excitation-relaxation dynamics by modifying the ability of the system to establish globally connected excitation. Simultaneously, the global dipole signal directly encodes transitions between regimes with and without a globally connected excited state.