  Self-induced stochastic resonance (SISR) is a subtle resonance mechanism
requiring a nontrivial scaling limit between the stochastic and the
deterministic timescales of an excitable system, leading to the emergence of a
limit cycle behavior which is absent without noise. All previous studies on
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 Levy timescale (that
follows a power law, unlike Gaussian noise that follows Kramers law) and the
deterministic timescale (controlled by the singular parameter) can also induce
a strong SISR. In addition, it is shown that the degree of SISR induced by Levy
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
find applications in designing neuromorphic circuits operating in noisy
regimes.
