Traveling Wavefronts in an Antidiffusion Lattice Nagumo Model

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Issue Date
2011-06-06Author
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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Show full item recordAbstract
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.
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This is the published version, also available here: http://dx.doi.org/10.1137/100819461.
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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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