Areduced gradient description of stochastic-resonant spatiotemporal patterns in a FitzHugh?Nagumo ring with electric inhibitory coupling

Abstract

We study the synchronization (sync) properties of a ring of N units with excitable FitzHugh?Nagumo dynamics, when the inhibitor fields of nearest-neighbor units are coupled diffusively (electric coupling). The system is submitted to a common subthreshold adiabatic signal S(t), and independent Gaussian white noises with common variance η. By running numerical integrations with increasing η, we observe the excitation activity to become spatiotemporally self-organized, until η is so strong that spoils sync. By means of a two-cell model and projecting the dynamics along the slow manifolds, we obtain a (signal-dependent) potential landscape which explains qualitatively the sync regime, and whose barrier heights give a good estimate of the optimal noise intensity.