Synchronization of the Stochastic Fitzhugh-Nagumo Equations to Periodic Forcing ( * ) .

The Fitzhugh-Nagumo equations (FHN) provide a simple description of the dynamics of a large class of neurons. We characterize synchronization and stochastic resonance in this model using two complementary points of view: the signal-to-noise ratio (SNR), and the absolute as well as normalized peak heights of the interspike interval histograms (ISIHs). At low stimulus frequencies, multiple f'Lrings can occur during one period, while at high frequencies, the refractoriness precludes firing at every cycle. The behaviors of the SNR and ISIHs are thus investigated at low, medium and high frequencies to illustrate special synchronization properties of the FHN system. In particular, the behavior of the SNR vs. noise is found to be similar for forcing amplitudes just below and above that at which a 2 : 1 deterministic phase-locked f'kring solution becomes stable. Our results rely on an accurate method of estimation of the power spectrum of the point process formed by the fh'ing times. A theoretical analysis for the shape of the simulated power spectra is also presented.