Stochastic dynamics of the FitzHugh-Nagumo neuron model through a modified Van der Pol equation with fractional-order term and Gaussian white noise excitation

Guimfack, Boris Anicet; Tabi, Conrad Bertrand; Mohamadou, Alidou; Kofané, Timoléon Crépin

doi:10.3934/dcdss.2020397

Cited by 2 publications

(1 citation statement)

References 45 publications

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“…The stochastic dynamics and approximations of non‐autonomous SFHN model in

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is established by Zhao 19 . Guimfack et al 20 studied stochastic response of fractional order FHN system with the Gaussian white noise. Numerical scheme and stability analysis are discussed by Yasin et al 21 using finite difference method.…”

Section: Introductionmentioning

confidence: 99%

Non‐instantaneous impulsive stochastic FitzHugh–Nagumo equation with fractional Brownian motion

Durga

Malik

2023

Math Methods in App Sciences

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This article is devoted to examine the exponential behavior of stochastic FitzHugh-Nagumo equation in Hilbert space. Initially, the proposed model is reformulated into an abstract space, and the existence of mild solution is constructed by employing Mönch fixed-point theorem and Hausdorff measure of non-compactness. Furthermore, suitable conditions are developed to prove the proposed model's exponential behavior which reflects the stable generation and transmission of electric signal in neurons. At last, an example is presented to verify the established theoretical concepts.

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“…The stochastic dynamics and approximations of non‐autonomous SFHN model in

{R}&#x0005E;N

Section: Introductionmentioning

confidence: 99%

Non‐instantaneous impulsive stochastic FitzHugh–Nagumo equation with fractional Brownian motion

Durga

Malik

2023

Math Methods in App Sciences

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Identification method for a fractional-order system in terms of equivalent dynamic properties

Yuan,

Xu,

Liu

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we introduce an efficient method for identifying fractional dynamic systems using extended sparse regression and cross-validation techniques. The former identifies equations that fit the data with varying candidate functions, while the latter determines the optimal equation with the fewest terms yet ensuring accuracy. The identified optimal equation is expected to share the same dynamic properties as the original fractional system. Unlike previous studies focusing on efficiently computing fractional terms, this strategy addresses dynamic analysis from a data perspective. Importantly, in the proposed method, we treat the fractional order as a variable to account for its impact on the dynamic properties of the identified equation. This treatment enables the identified equation to successfully capture dynamic behaviors when the fractional order changes. We validate the effectiveness of the method using three classical fractional-order systems as well as an energy harvesting system. Interestingly, we find that, although the identified equations do not contain non-local terms like the original fractional-order systems, they exhibit the same stochastic P-bifurcation phenomena. In other words, we construct an equivalent equation without memory properties, sharing the dynamic properties with the original system.

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Stochastic dynamics of the FitzHugh-Nagumo neuron model through a modified Van der Pol equation with fractional-order term and Gaussian white noise excitation

Cited by 2 publications

References 45 publications

Non‐instantaneous impulsive stochastic FitzHugh–Nagumo equation with fractional Brownian motion

Non‐instantaneous impulsive stochastic FitzHugh–Nagumo equation with fractional Brownian motion

Identification method for a fractional-order system in terms of equivalent dynamic properties

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