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Hupkes, H.J., Pelinovsky, D. and Sandstede, B. (2011) Propagation Failure in the Discrete Nagumo Equation. Proceedings of the American Mathematical Society, 139, 3537-3551.
https://doi.org/10.1090/S0002-9939-2011-10757-3

has been cited by the following article:

• TITLE: Propagation and Pinning of Travelling Wave for Nagumo Type Equation

  AUTHORS: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

  KEYWORDS: Operator Splitting, Travelling Wave, Piecewise Reaction, Nagumo Equation, Pinning, Finite Differences

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.3, March 28, 2024

  ABSTRACT: In this paper, we study the propagation and its failure to propagate (pinning) of a travelling wave in a Nagumo type equation, an equation that describes impulse propagation in nerve axons that also models population growth with Allee effect. An analytical solution is derived for the traveling wave and the work is extended to a discrete formulation with a piecewise linear reaction function. We propose an operator splitting numerical scheme to solve the equation and demonstrate that the wave either propagates or gets pinned based on how the spatial mesh is chosen.