Spirals in Excitable Chemical Media: From Archimedian to Non-Archimedian Geometry

Abstract

Propagation phenomena under far from equilibrium conditions are observed in many nonlinear physical and biological systems (for an overview see [1]). In particular, travelling waves are a characteristic spatio-temporal pattern occurring in excitable media. They have been studied in much detail in chemical model systems, mostly in the Belousov-Zhabotinskii (BZ) reaction prepared with excitable reaction kinetics [2,3]. In this solution malonic acid is oxidized and decarboxylized by bromous compounds to form organic products. The reaction takes place in the presence of a metal ion redox catalyst, usually ferroin, which changes its colour during the excitation, involving a transition from the reduced to the oxidized state. Thus, in a thin solution layer chemical waves are detectable by their blue fronts indicating the presence of the oxidizing state ferriin, which travel through a quiescent red solution layer where ferroin, the reduced form of the catalyst, prevails. The spatial distribution of the catalyst concentration in such waves can be determined quantitatively since devices of ID and 2D spectrophotometry have become available [4–6].