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    Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations

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    Issue Date
    2006-07-31
    Author
    Vateman, Michael D.
    Van Vleck, Erik S.
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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    Abstract
    We consider a coupled system of discrete Nagumo equations and derive traveling wave solutions to this system using McKean's caricature of the cubic. A certain form of this system is used to model ephaptic coupling between pairs of nerve axons. We study the difference $g(c)=a_1-a_2$ between the detuning parameters $a_i$ that is required to make both waves move at the same speed c. Of particular interest is the effect of a coupling parameter $\alpha$ and an "alignment" parameter A on the function g. Numerical investigation indicates that for fixed A, there exists a time delay value $\beta$ that results in $g=0$, and for large enough wave speeds, multiple such $\beta$ values exist. Also, numerical results indicate that the perturbation of $\alpha$ away from zero will yield additional solutions with positive wave speed when $A={1\over 2}$. We employ both analytical and numerical results to demonstrate our claims.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1137/050624352.
    URI
    http://hdl.handle.net/1808/17248
    DOI
    https://doi.org/10.1137/050624352
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Batemen, Michael D. & Van Vleck, Erik."Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations." (2006) SIAM J. Appl. Math., 66(3), 945–976. (32 pages). http://dx.doi.org/10.1137/050624352.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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