  Motivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a
caricature of excitable systems, in this paper we study kink-antikink dynamics
in the perhaps simplest PDE model of excitable media given by the scalar
reaction diffusion-type $\theta$-equations for excitable angular phase
dynamics. On the one hand, we qualitatively study geometric kink positions
using the comparison principle and the theory of terraces. This yields the
minimal initial distance as a global lower bound, a well-defined sequence of
collision data for kinks- and antikinks, and implies that periodic pure kink
sequences are asymptotically equidistant. On the other hand, we study
metastable dynamics of finitely many kinks using weak interaction theory for
certain analytic kink positions, which admits a rigorous reduction to ODE. By
blow-up type singular rescaling we show that distances become ordered in finite
time, and eventually diverge. We conclude that diffusion implies a loss of
information on kink distances so that the entropic complexity based on
positions and collisions in the GHCA does not simply carry over to the PDE
model.
