Lévy noise-induced self-induced stochastic resonance in a memristive neuron

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 $$\alpha $$ α -stable Lévy process (with value increasing as a power $$\sigma ^{-\alpha }$$ σ - α of the noise amplitude $$\sigma $$ σ , 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.