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    Traveling Wavefronts in an Antidiffusion Lattice Nagumo Model

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    VanVleck_SIAMADS_10(3)921.pdf (1.377Mb)
    Issue Date
    2011-06-06
    Author
    Brucal-Hallare, Maila
    Van Vleck, Erik S.
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
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    Abstract
    We consider a system of lattice Nagumo equations with cubic nonlinearity, but with a negative discrete diffusion coefficient. We are interested in the existence, uniqueness, stability, and nonexistence of the traveling wavefront solutions of this system, and we shall call this problem the antidiffusion lattice Nagumo problem. By rewriting this system as a spatially periodic system with inhomogeneous but positive periodic diffusion coefficients and periodic nonlinearities, we uncover a rich solution behavior that includes many possible connecting orbits in the antidiffusion case. Second, we observe the presence of bistable and monostable dynamics. In the bistable region, we study the phenomenon of propagation of failure while in the monostable region, we compute the minimum wave speed.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1137/100819461.
    URI
    http://hdl.handle.net/1808/17244
    DOI
    https://doi.org/10.1137/100819461
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Brucal-Hallare, Maila & Van Vleck, Erik. "Traveling Wavefronts in an Antidiffusion Lattice Nagumo Model." (2011) SIAM J. Appl. Dyn. Syst., 10(3), 921–959. (39 pages). http://dx.doi.org/10.1137/100819461.

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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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