A fractional-order improved FitzHugh-Nagumo neuron model

doi:10.1088/1674-1056/ad8a46

中国物理B ›› 2025, Vol. 34 ›› Issue (1): 18704-018704.doi: 10.1088/1674-1056/ad8a46

A fractional-order improved FitzHugh-Nagumo neuron model

Pushpendra Kumar^1,2,†,‡ and Vedat Suat Erturk^3,†

1 Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey;
2 Department of Mathematics, Mathematics Research Center, Near East University TRNC, Mersin 10, Turkey;
3 Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Atakum-55200, Samsun, Turkey

收稿日期:2024-07-02 修回日期:2024-09-09 接受日期:2024-10-23 出版日期:2024-12-06 发布日期:2024-12-12
通讯作者: Pushpendra Kumar E-mail:kumarsaraswatpk@gmail.com

A fractional-order improved FitzHugh-Nagumo neuron model

Pushpendra Kumar^1,2,†,‡ and Vedat Suat Erturk^3,†

1 Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey;
2 Department of Mathematics, Mathematics Research Center, Near East University TRNC, Mersin 10, Turkey;
3 Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Atakum-55200, Samsun, Turkey

Received:2024-07-02 Revised:2024-09-09 Accepted:2024-10-23 Online:2024-12-06 Published:2024-12-12
Contact: Pushpendra Kumar E-mail:kumarsaraswatpk@gmail.com

摘要/Abstract

摘要： We propose a fractional-order improved FitzHugh-Nagumo (FHN) neuron model in terms of a generalized Caputo fractional derivative. Following the existence of a unique solution for the proposed model, we derive the numerical solution using a recently proposed L1 predictor-corrector method. The given method is based on the L1-type discretization algorithm and the spline interpolation scheme. We perform the error and stability analyses for the given method. We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns, chaotic patterns, and quasi-periodic patterns. The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics, which are inherent to many biological systems.

关键词: FitzHugh-Nagumo neuron model, generalized Caputo fractional derivative, L1 predictor-corrector method, stability, error estimation

Abstract: We propose a fractional-order improved FitzHugh-Nagumo (FHN) neuron model in terms of a generalized Caputo fractional derivative. Following the existence of a unique solution for the proposed model, we derive the numerical solution using a recently proposed L1 predictor-corrector method. The given method is based on the L1-type discretization algorithm and the spline interpolation scheme. We perform the error and stability analyses for the given method. We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns, chaotic patterns, and quasi-periodic patterns. The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics, which are inherent to many biological systems.

Key words: FitzHugh-Nagumo neuron model, generalized Caputo fractional derivative, L1 predictor-corrector method, stability, error estimation

中图分类号: (Neuronal network dynamics)

87.19.lj

45.10.Hj (Perturbation and fractional calculus methods) 82.40.Bj (Oscillations, chaos, and bifurcations)

Pushpendra Kumar and Vedat Suat Erturk. A fractional-order improved FitzHugh-Nagumo neuron model[J]. 中国物理B, 2025, 34(1): 18704-018704.

Pushpendra Kumar and Vedat Suat Erturk. A fractional-order improved FitzHugh-Nagumo neuron model[J]. Chin. Phys. B, 2025, 34(1): 18704-018704.

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A fractional-order improved FitzHugh-Nagumo neuron model

A fractional-order improved FitzHugh-Nagumo neuron model

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