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Regul. Chaotic Dyn., 2018, Volume 23, Issue 2, Pages 152–160 (Mi rcd315)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic and Exact Solutions of the FitzHugh–Nagumo Model

Nikolay A. Kudryashov

Department of Applied Mathematics, National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia

Abstract: The standard FitzHugh–Nagumo model for description of impulse from one neuron to another is considered. The system of equations is transformed to a nonlinear second-order ordinary differential equation. It is shown that the differential equation does not pass the Painlevé test in the general case and the general solution of this equation does not exist. The simplest solutions of the system of equations are found. The second-order differential equation is transformed to another asymptotic equation with the general solution expressed via the Jacobi elliptic function. This transformation allows us to obtain the asymptotic solutions of the FitzHugh–Nagumo model. The perturbed FitzHugh–Nagumo model is studied as well. Taking into account the simplest equation method, the exact solutions of the perturbed system of equations are found. The asymptotic solutions of the perturbed model are presented too. The application of the exact solutions for construction of the neural networks is discussed.

Keywords: neuron, FitzHugh–Nagumo model, system of equations, Painelevé test, exact solution

Funding Agency Grant Number
Russian Science Foundation 17-71-20111
This work was supported by the Research Science Foundation grant 17-71-20111 “Study and justification of mechanisms for spiking neural networks learning based on synaptic plasticity in order to create biologically inspired nonlinear information models capable of solving practical tasks”.


DOI: https://doi.org/10.1134/S1560354718020028

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Bibliographic databases:

MSC: 34M05, 34E10
Received: 01.11.2017
Accepted:22.12.2017
Language:

Citation: Nikolay A. Kudryashov, “Asymptotic and Exact Solutions of the FitzHugh–Nagumo Model”, Regul. Chaotic Dyn., 23:2 (2018), 152–160

Citation in format AMSBIB
\Bibitem{Kud18}
\by Nikolay A. Kudryashov
\paper Asymptotic and Exact Solutions of the FitzHugh–Nagumo Model
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 2
\pages 152--160
\mathnet{http://mi.mathnet.ru/rcd315}
\crossref{https://doi.org/10.1134/S1560354718020028}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045003274}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nikolay A. Kudryashov, “Exact Solutions and Integrability of the Duffing–Van der Pol Equation”, Regul. Chaotic Dyn., 23:4 (2018), 471–479  mathnet  crossref  mathscinet
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