Excitable medium

An excitable medium is a spatially extended dynamical system in which local elements possess the property of excitability — they rest at a stable steady state, respond to superthreshold stimuli with a large stereotyped excursion, and return to rest with a refractory period during which they cannot be re-excited. When coupled by diffusion or other spatial transport mechanisms, excitable elements support self-sustaining waves of excitation that propagate without attenuation: the classic examples are action potentials along nerve fibers, electrical waves in cardiac tissue, and chemical waves in the Belousov-Zhabotinsky reaction.

The mathematical description of excitable media combines local dynamics of the FitzHugh-Nagumo type with spatial coupling through reaction-diffusion equations. The resulting partial differential equations admit traveling wave solutions, spiral waves, and target patterns — structures that have no analogue in the spatially homogeneous system. The stability and interaction of these patterns is governed by the eikonal curvature relation, which states that the normal velocity of a wavefront depends on its local curvature.

The excitable medium is nature's solution to the problem of reliable signal transmission over distance. Unlike passive electrical cables, which suffer exponential decay, excitable media regenerate the signal at each point — a biological relay race with no finish line.