Noise-sustained synchronization between electrically coupled FitzHugh–Nagumo networks

We investigate the capability of electrical synapses to transmit the noise-sustained network activity from one network to another. The particular setup we consider is two identical rings with excitable FitzHugh–Nagumo cell dynamics and nearest-neighbor antiphase intra-ring coupling, electrically coupled between corresponding nodes. The whole system is submitted to independent local additive Gaussian white noises with common intensity η, but only one ring is externally forced by a global adiabatic subthreshold harmonic signal. We then seek conditions for a particular noise level to promote synchronized stable firing patterns. 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 between networks for a given value of the electric coupling strength. By means of a four-cell model and calculating the stationary probability distribution, we obtain a (signal-dependent) non-equilibrium potential landscape which explains qualitatively the observed regimes, and whose barrier heights give a good estimate of the optimal noise intensity for the sync between networks.