Phase mappings from diffusion-coupled excitable chemical systems

Abstract

Dynamics of a cascade of two diffusion-coupled excitable units periodically perturbed by pulses applied to the first cell is examined. Firing sequences experimentally found in a chemical system constituted by two coupled stirred cells with the Belousov-Zhabotinskii (BZ) reaction are modelled on two levels. A phase mapping of an abstract piecewise linear excitable two-cell system is derived and its dynamics examined in detail. The functional form of this map combined with local excitation dynamics extracted from a realistic model of the BZ kinetics is used to formulate a semi-empirical model directly applicable to the experimental BZ system. The frequency of firings in the second cell can be either equal to that in the first cell - a complete propagation of the excitation, or smaller - a propagation failure. Complex patterns of transitions between the two dynamic modes found in experiments are well predicted by the semi-empirical model and, surprisingly, by the abstract model as well, pointing to a generic nature of the patterns.