Transition from a strong to a weak coherence resonance in phase neuron models

초록

We study the dynamical response to noise in the one-dimensional type-I phase neuron model with a parameter alpha (0 <= alpha <= 1) tuning the degree of multiplication in the noise. For alpha = 0, the phase model is just the Adler equation, while it becomes the canonical type-I theta model for alpha = 1. For the subthreshold case, the effect of noise on the oscillating characteristics is investigated by increasing alpha from 0. A characteristic correlation time tau(c) has a maximum at some optimal noise intensity D*, independently of alpha. However, the phase model exhibits spectrally a coherent or incoherent response to noise, depending on the value of a. For alpha = 0, a spectrally coherent response to noise occurs in the Adler equation (i.e., noise-induced peaks appear in the output power spectrum) and is maximized near D*. Thus, the Adler equation exhibits a "strong" coherence resonance (i.e., a maximal correlation occurs along with a spectral coherence resonance). However, as a increases and passes a threshold value alpha*, such a spectrally coherent response ceases because the noise-induced peaks disappear from the output power spectrum for alpha > alpha*. Thus, the phase model for alpha > alpha* exhibits a "weak" coherence resonance (i.e., a maximal correlation occurs without any spectral coherence).

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