Dynamical analysis of the FitzHugh–Nagumo oscillations through a modified Van der Pol equation with fractional-order derivative term

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Abstract

The nonlinear dynamics of action potentials in the FitzHugh–Nagumo model is addressed using a modified Van der Pol equation with fractional-order derivative and periodic parametric excitation. Through the averaging method, the approximately analytical and the steady-state solutions are obtained, and their existence condition and stability are investigated. Analytical calculations are confirmed numerically and one insists on the coupled effects of the parametric excitation, system parameters and fractional-order parameter to discuss the various dynamical behaviors of the studied system. Mainly, the fractional-order derivative modifies the features of the amplitude–frequency curves. This might be an efficient tool to control the dynamics of the action potentials, with important biological implications that are discussed.
Original languageEnglish
Pages (from-to)173-178
Number of pages6
JournalInternational Journal of Non-Linear Mechanics
Volume105
DOIs
Publication statusPublished - Oct 1 2018

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Van Der Pol Equation
Modified Equations
Fractional Order
Parametric Excitation
Action Potential
Oscillation
Derivatives
Derivative
Term
Averaging Method
Steady-state Solution
Dynamical Behavior
Order Parameter
Nonlinear Dynamics
Curve
Model

Cite this

@article{4213778981e14ce3b334fd5c15d139f2,
title = "Dynamical analysis of the FitzHugh–Nagumo oscillations through a modified Van der Pol equation with fractional-order derivative term",
abstract = "The nonlinear dynamics of action potentials in the FitzHugh–Nagumo model is addressed using a modified Van der Pol equation with fractional-order derivative and periodic parametric excitation. Through the averaging method, the approximately analytical and the steady-state solutions are obtained, and their existence condition and stability are investigated. Analytical calculations are confirmed numerically and one insists on the coupled effects of the parametric excitation, system parameters and fractional-order parameter to discuss the various dynamical behaviors of the studied system. Mainly, the fractional-order derivative modifies the features of the amplitude–frequency curves. This might be an efficient tool to control the dynamics of the action potentials, with important biological implications that are discussed.",
author = "Tabi, {Conrad Bertrand}",
year = "2018",
month = "10",
day = "1",
doi = "10.1016/j.ijnonlinmec.2018.05.026",
language = "English",
volume = "105",
pages = "173--178",
journal = "International Journal of Non-Linear Mechanics",
issn = "0020-7462",
publisher = "Elsevier Limited",

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TY - JOUR

T1 - Dynamical analysis of the FitzHugh–Nagumo oscillations through a modified Van der Pol equation with fractional-order derivative term

AU - Tabi, Conrad Bertrand

PY - 2018/10/1

Y1 - 2018/10/1

N2 - The nonlinear dynamics of action potentials in the FitzHugh–Nagumo model is addressed using a modified Van der Pol equation with fractional-order derivative and periodic parametric excitation. Through the averaging method, the approximately analytical and the steady-state solutions are obtained, and their existence condition and stability are investigated. Analytical calculations are confirmed numerically and one insists on the coupled effects of the parametric excitation, system parameters and fractional-order parameter to discuss the various dynamical behaviors of the studied system. Mainly, the fractional-order derivative modifies the features of the amplitude–frequency curves. This might be an efficient tool to control the dynamics of the action potentials, with important biological implications that are discussed.

AB - The nonlinear dynamics of action potentials in the FitzHugh–Nagumo model is addressed using a modified Van der Pol equation with fractional-order derivative and periodic parametric excitation. Through the averaging method, the approximately analytical and the steady-state solutions are obtained, and their existence condition and stability are investigated. Analytical calculations are confirmed numerically and one insists on the coupled effects of the parametric excitation, system parameters and fractional-order parameter to discuss the various dynamical behaviors of the studied system. Mainly, the fractional-order derivative modifies the features of the amplitude–frequency curves. This might be an efficient tool to control the dynamics of the action potentials, with important biological implications that are discussed.

UR - http://www.mendeley.com/research/dynamical-analysis-fitzhughnagumo-oscillations-through-modified-van-der-pol-equation-fractionalorder

U2 - 10.1016/j.ijnonlinmec.2018.05.026

DO - 10.1016/j.ijnonlinmec.2018.05.026

M3 - Article

VL - 105

SP - 173

EP - 178

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

ER -