Excitability at the interface

An excitable medium, like a beating heart, is normally thought of as a collection of elements that can individually display behaviors like spiking or pacemaking. Here, we show the following: two media that are individually non-excitable can become excitable at their interface when a fast degree of freedom is diffusively coupled. We connect this phenomenon to topological properties of the underlying nonlinear, heterogeneous reaction-diffusion equations. We then explicitly demonstrate this principle using simple models from electrophysiology, population dynamics, and chemical oscillators. Our findings provide a mathematical basis for interpreting recent experiments in electrophysiology [Ori et al. (2022)], and for controlling pattern formation and nonlinear waves across diverse physical platforms.