Exact nonequilibrium potential for the FitzHugh-Nagumo model in the excitable and bistable regimes

We obtain an analytically exact nonequilibrium potential for the space-independent FitzHugh-Nagumo model, valid in the excitable and bistable regimes (in the limit of small noise). This potential allows us to characterize the nature of the barrier in the excitable regime and, after subjecting the system to a modulated weak signal that rocks the potential inducing the phenomenon of stochastic resonance, to calculate the signal to-noise ratio in the bistable regime.