Effect of noise on the tuning properties of excitable systems

We analyze the effect of additive dynamical noise on simple phase-locking patterns in the Fitzhugh–Nagumo (FHN) two-dimensional system in the excitable regime. In the absence of noise, the response amplitude for this system displays a classical resonance as a function of driving frequency. This translates into V-shaped tuning curves, which represent the amplitude threshold for one firing per cycle as a function of forcing frequency. We show that noise opens up these tuning curves at mid-to-low frequencies. We explain this numerical result analytically using a heuristic form for the firing rate that incorporates the frequency dependence of the subthreshold voltage response. We also present stochastic phase-locking curves in the noise intensity-forcing period subspace of parameter space. The relevance of our findings for the tuning of electroreceptors of weakly electric fish and their encoding of amplitude modulations of high frequency carriers are briefly discussed. Our study shows that, in certain contexts, it is essential to take into account the frequency sensitivity of neural responses and their modification by sources of noise.