Sheet Excitability and Nonlinear Wave Propagation

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Abstract
In the Xenopus laevis oocyte, calcium ion channels are clustered in a thin shell. Motivated by this morphology, we study a general class of reaction-diffusion systems that include most of the well-known models that support wave propagation but restricting excitability to a “sheet” of codimension 1. We find waves that undergo propagation failure with increasing diffusion coefficient and a scaling regime in which the wave speed is independent of it.