A reduced gradient description of stochastic-resonant spatiotemporal patterns in a FitzHugh–Nagumo ring with electric inhibitory coupling

• FHN ring with diffusive inhibitory coupling exhibits dynamic antiphase states (APS).
• APS coherence runs through a maximum as function of noise variance.
• Dynamics captured by two-cell model and projection along slow manifolds.
• Resulting system is gradient. Barrier height close to optimal noise variance.
• Two-cell system overtakes barrier towards APS, returning deterministically.

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)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.