A fractional-order improved FitzHugh-Nagumo neuron model

doi:10.1088/1674-1056/ad8a46

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.

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

Received: 02 July 2024
Revised: 09 September 2024
Accepted manuscript online: 23 October 2024

PACS:	87.19.lj	(Neuronal network dynamics)
	45.10.Hj	(Perturbation and fractional calculus methods)
	82.40.Bj	(Oscillations, chaos, and bifurcations)

Corresponding Authors: Pushpendra Kumar
E-mail: kumarsaraswatpk@gmail.com

Cite this article:

Pushpendra Kumar and Vedat Suat Erturk A fractional-order improved FitzHugh-Nagumo neuron model 2025 Chin. Phys. B 34 018704

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A fractional-order improved FitzHugh-Nagumo neuron model

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