Structure Formation in Excitable Media

Abstract

Excitable media are widespread in nature. They play important roles in physics and chemistry as well as in biology and medicine. Applications comprise phenomena as diverse as the pigmentation patterns of vertebrate skins or of shells of molluscs, cardiac arrythmia, formation of galaxies, energy metabolism, aggregation of slime mold amoebae, spatio-temporal EEG-patterns and circadian rhythms in physiology and biological populations (cf. [6], [10], [11]). The most prominent feature of an excitable medium, of course, is its ability to receive and distribute excitation. The main phenomenon observed in such media, therefore, is that of waves formed by the propagation of excitation gradients. As the examples above might suggest, the supporting medium need not be a continuum but can also have discrete structure. The former, as a rule, is modeled by means of partial differential equations, the latter more often by cellular automata. Obviously, many reaction-diffusion and aggregation processes are intimately connected with the phenomena encountered in excitable media.