Stochastic dynamics of the fitzhugh-nagumo neuron model through a modified van der pol equation with fractional-order term and gaussian white noise excitation

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

doi:10.3934/DCDSS.2020397

Stochastic dynamics of the fitzhugh-nagumo neuron model through a modified van der pol equation with fractional-order term and gaussian white noise excitation

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

Research output: Contribution to journal › Article › peer-review

Abstract

The stochastic response of the FitzHugh-Nagumo model is addressed using a modified Van der Pol (VDP) equation with fractional-order derivative and Gaussian white noise excitation. Via the generalized harmonic balance method, the term related to fractional derivative is splitted into the equivalent quasi-linear dissipative force and quasi-linear restoring force, leading to an equivalent VDP equation without fractional derivative. The analytical solutions for the equivalent stochastic equation are then investigated through.

Original language	English
Pages (from-to)	2229-2243
Number of pages	15
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	14
Issue number	7
DOIs	https://doi.org/10.3934/DCDSS.2020397
Publication status	Published - Jul 2021

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/DCDSS.2020397

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@article{c971abb8222c496dae6aaee5c1cb3191,

title = "Stochastic dynamics of the fitzhugh-nagumo neuron model through a modified van der pol equation with fractional-order term and gaussian white noise excitation",

abstract = "The stochastic response of the FitzHugh-Nagumo model is addressed using a modified Van der Pol (VDP) equation with fractional-order derivative and Gaussian white noise excitation. Via the generalized harmonic balance method, the term related to fractional derivative is splitted into the equivalent quasi-linear dissipative force and quasi-linear restoring force, leading to an equivalent VDP equation without fractional derivative. The analytical solutions for the equivalent stochastic equation are then investigated through.",

author = "Guimfack, \{Boris Anicet\} and Tabi, \{Conrad Bertrand\} and Alidou Mohamadou and Kofan{\'e}, \{Timol{\'e}on Cr{\'e}pin\}",

note = "Funding Information: The work of CBT was supported by the Botswana International University of Science and Technology under the grant DVC/RDI/2/1/16I (25). CBT thanks the Kavli Institute for Theoretical Physics (KITP), University of California Santa Barbara (USA), where this work was supported in part by the National Science Foundation Grant no.NSF PHY-1748958 and NIH Grant no.R25GM067110. ∗ Corresponding author: [email protected] (C. B. Tabi). Publisher Copyright: {\textcopyright} 2021 American Institute of Mathematical Sciences. All rights reserved.",

year = "2021",

month = jul,

doi = "10.3934/DCDSS.2020397",

language = "English",

volume = "14",

pages = "2229--2243",

journal = "Discrete and Continuous Dynamical Systems - Series S",

issn = "1937-1632",

publisher = "American Institute of Mathematical Sciences",

number = "7",

}

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 et al.
In: Discrete and Continuous Dynamical Systems - Series S, Vol. 14, No. 7, 07.2021, p. 2229-2243.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Stochastic dynamics of the fitzhugh-nagumo neuron model through a modified van der pol equation with fractional-order term and gaussian white noise excitation

AU - Guimfack, Boris Anicet

AU - Tabi, Conrad Bertrand

AU - Mohamadou, Alidou

AU - Kofané, Timoléon Crépin

N1 - Funding Information: The work of CBT was supported by the Botswana International University of Science and Technology under the grant DVC/RDI/2/1/16I (25). CBT thanks the Kavli Institute for Theoretical Physics (KITP), University of California Santa Barbara (USA), where this work was supported in part by the National Science Foundation Grant no.NSF PHY-1748958 and NIH Grant no.R25GM067110. ∗ Corresponding author: [email protected] (C. B. Tabi). Publisher Copyright: © 2021 American Institute of Mathematical Sciences. All rights reserved.

PY - 2021/7

Y1 - 2021/7

N2 - The stochastic response of the FitzHugh-Nagumo model is addressed using a modified Van der Pol (VDP) equation with fractional-order derivative and Gaussian white noise excitation. Via the generalized harmonic balance method, the term related to fractional derivative is splitted into the equivalent quasi-linear dissipative force and quasi-linear restoring force, leading to an equivalent VDP equation without fractional derivative. The analytical solutions for the equivalent stochastic equation are then investigated through.

AB - The stochastic response of the FitzHugh-Nagumo model is addressed using a modified Van der Pol (VDP) equation with fractional-order derivative and Gaussian white noise excitation. Via the generalized harmonic balance method, the term related to fractional derivative is splitted into the equivalent quasi-linear dissipative force and quasi-linear restoring force, leading to an equivalent VDP equation without fractional derivative. The analytical solutions for the equivalent stochastic equation are then investigated through.

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JO - Discrete and Continuous Dynamical Systems - Series S

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IS - 7

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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

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