Oscillating Reaction-Diffusion Spots

Reaction-diffusion systems produce a variety of patterns such as spots, labyrinths, and rotating spirals. Circular spots may be stationary or unstable to oscillating motion. The oscillations are sometimes steady but may lead to collapsing or infinitely expanding spots. Using a singular perturbation technique we derive a set of ordinary differential equations for the dynamics of circular spots. These equations are considerably simpler to study than the underlying reaction-diffusion model and quantitatively reproduce the same dynamics. 1 Introduction The discovery of replicating spots, first in models [1] and then in chemical experiments [2, 3] sparked renewed interest in the formation of localized reaction-diffusion patterns. In addition to replicating spots, oscillating circular spots have also been found in the Ferrocyanide-Iodate-Sulfite reaction [4]. One kind of spot is formed from interactions with the circular boundary of the chemical reactor. It may be stationary or become uns..