Dynamical complexity of FitzHugh–Nagumo neuron model driven by Lévy noise and Gaussian white noise

Guo, Yongfeng; Wang, Linjie; Dong, Qiang; Lou, Xiaojuan

doi:10.1016/j.matcom.2020.09.026

Cited by 9 publications

(2 citation statements)

References 31 publications

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“…Furthermore, several studies on stochastic systems have departed from Gaussian to Lévy processes and compared their effects. For example, in [47], the study of the stochastic payoff variations in the spatial prisoner's dilemma game is presented; in [50], the neuron competition models; and in [51], the statistical complexity and normalized Shannon entropy of the FitzHugh-Nagumo neuron model. Motivated by the relevance of Lévy processes in neural systems explained above, this paper focuses on SISR in a memristive neuron perturbed by a Lévy noise-a setting that has not been considered before.…”

Section: Introductionmentioning

confidence: 99%

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

Yamakou

Tran

2021

Nonlinear Dyn

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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.

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Section: Introductionmentioning

confidence: 99%

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

Yamakou

Tran

2021

Nonlinear Dyn

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“…Several studies on stochastic systems have departed from Gaussian to Lévy processes and compared their effects. For example, in [63], the study of the stochastic payoff variations in the spatial prisoner's dilemma game is presented; in [18], the neuron competition models; and in [24], the statistical complexity and normalized Shannon entropy of the FitzHugh-Nagumo neuron model. In this paper, in a similar fashion, we study SISR in a memristive neuron perturbed by a Lévy white noise.…”

Section: Introductionmentioning

confidence: 99%

Lévy Noise-induced Self-induced Stochastic Resonance in a Memristive Neuron

Yamakou

Tran

2021

Preprint

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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 mean escape timescale of an α-stable Lévy process (with value increasing as a power σ-α of the noise amplitude σ, unlike the mean escape timescale of a Gaussian process with the value increasing as in 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 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 find applications in designing neuromorphic circuits operating in noisy regimes.

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Dynamical analysis of an improved FitzHugh-Nagumo neuron model with multiplier-free implementation

Chen

et al. 2023

Nonlinear Dyn

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Dynamical complexity of FitzHugh–Nagumo neuron model driven by Lévy noise and Gaussian white noise

Cited by 9 publications

References 31 publications

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

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

Lévy Noise-induced Self-induced Stochastic Resonance in a Memristive Neuron

Dynamical analysis of an improved FitzHugh-Nagumo neuron model with multiplier-free implementation

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