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

Journal article

Authors/Editors

Tabi, Condrad

Research Areas

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Publication Details

Author list: Tabi CB

Publisher: Elsevier

Place: OXFORD

Publication year: 2018

Journal: International Journal of Non-Linear Mechanics (0020-7462)

Journal acronym: INT J NONLIN MECH

Volume number: 105

Start page: 173

End page: 178

Number of pages: 6

ISSN: 0020-7462

Languages: English-Great Britain (EN-GB)

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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.

Keywords

Amplitude-frequency curves, FitzHugh-Nagumo model, Fractional-order derivatives, Primary resonance, Van der Pol oscillator

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