Abstract
All previous studies on self-induced stochastic resonance (SISR) in neural systems have only considered the idealized Gaussian white noise. Moreover, these studies have ignored one electrophysiological aspect of the nerve cell: its memristive properties. In this paper, first, we show that in the excitable regime, the asymptotic matching of the deterministic timescale and mean escape timescale of an alpha -stable Lévy process (with value increasing as a power sigma ^{-alpha } of the noise amplitude sigma , unlike the mean escape timescale of a Gaussian process which increases as in Kramers’ law) can also induce a strong SISR. In addition, it is shown that the degree of SISR induced by Lévy noise is not always higher than that of Gaussian noise. Second, we show that, for both types of noises, the two memristive properties of the neuron have opposite effects on the degree of SISR: the stronger the feedback gain parameter that controls the modulation of the membrane potential with the magnetic flux and the weaker the feedback gain parameter that controls the saturation of the magnetic flux, the higher the degree of SISR. Finally, we show that, for both types of noises, the degree of SISR in the memristive neuron is always higher than in the non-memristive neuron. Our results could guide hardware implementations of neuromorphic silicon circuits operating in noisy regimes.
Highlights
Noise is ubiquitous in neural systems and several studies have shown that it can play a constructive role in information processing [1,2,3,4,5,6,7,8,9,10]
We investigated and compared the mechanism of selfinduced stochastic resonance (SISR) induced by Lévy white noise and Gaussian white noise in a memristive FHN neuron
We showed that depending on the parameter values (α ∈ (0, 2) and β ∈ [−1, 1]) of the Lévy noise, the neuron could exhibit a very high degree of SISR with a minimum coefficient of variation as low as 0.000789, compared to 0.044 in the case of Gaussian noise
Summary
Noise is ubiquitous in neural systems and several studies have shown that it can play a constructive role in information processing [1,2,3,4,5,6,7,8,9,10]. In [68], the electromagnetic induction due to the memristive properties of the neurons has been shown to play important roles in the regulation of sleep wake cycle, where the time of wake up is delayed and fall asleep is advanced when the electromagnetic induction and its noise are considered. The effects of electromagnetic noise on the regulation have been shown to inhibit the neuronal discharge activities and change the time of wake up and fall asleep of the neurons It is well-accepted that the effects of the magnetic flux across the membrane of the cell should be considered when investigating the emergence of electrical activities and wave propagation in the nerve and cardiac cells [53,59]. The effect of the memristive properties of a neuron on Lévy and Gaussian noise-induced SISR are still elusive.
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