RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Nelin. Dinam.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Nelin. Dinam., 2019, Volume 15, Number 1, Pages 3–12 (Mi nd635)  

Nonlinear physics and mechanics

Analytical Properties and Solutions of the FitzHugh Rinzel Model

A. I. Zemlyanukhin, A. V. Bochkarev

Gagarin State Technical University, ul. Politekhnicheskaya 77, Saratov, 410054 Russia

Abstract: The FitzHugh Rinzel model is considered, which differs from the famous FitzHugh Nagumo model by the presence of an additional superslow dependent variable. Analytical properties of this model are studied. The original system of equations is transformed into a third-order nonlinear ordinary differential equation. It is shown that, in the general case, the equation does not pass the Painlevé test, and the general solution cannot be represented by Laurent series. Using the singular manifold method in terms of the Schwarzian derivative, an exact particular solution in the form of a kink is constructed, and restrictions on the coefficients of the equation necessary for the existence of such a solution are revealed. An asymptotic solution is obtained that shows good agreement with the numerical one. This solution can be used to verify the results in a numerical study of the FitzHugh Rinzel model.

Keywords: neuron, FitzHugh Rinzel model, singular manifold, exact solution, asymptotic solution

DOI: https://doi.org/10.20537/nd190101

Full text: PDF file (277 kB)
References: PDF file   HTML file

MSC: 34A05, 34A34
Received: 28.11.2018
Accepted:05.05.2019
Language:

Citation: A. I. Zemlyanukhin, A. V. Bochkarev, “Analytical Properties and Solutions of the FitzHugh Rinzel Model”, Nelin. Dinam., 15:1 (2019), 3–12

Citation in format AMSBIB
\Bibitem{ZemBoc19}
\by A. I. Zemlyanukhin, A. V. Bochkarev
\paper Analytical Properties and Solutions of the FitzHugh Rinzel Model
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 1
\pages 3--12
\mathnet{http://mi.mathnet.ru/nd635}
\crossref{https://doi.org/10.20537/nd190101}


Linking options:
  • http://mi.mathnet.ru/eng/nd635
  • http://mi.mathnet.ru/eng/nd/v15/i1/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:35
    Full text:11
    References:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019