Chemical wave responses to periodic stimuli in vulnerable excitable media

Abstract

A reaction–diffusion model of the Belousov–Zhabotinsky (BZ) reaction is studied in which an initial ‘conditioning’ wave (CW) propagates through an excitable system and sets up a region of inhomogeneity in which the system becomes spontaneously oscillatory. The subsequent oscillations in the concentrations of the intermediate species within this region can act as potential initiation sources for subsequent wave structures. The range of different responses is determined for a 1D configuration by numerical computation and the parameter combinations for the different types are located. Depending on the length of this region and the frequency of the spontaneous oscillations, the system may develop: sustained counter-propagating wave pairs, waves that propagate only in the opposite direction to the CW, waves that propagate only in the same direction as the CW, waves that propagate in alternating directions or no subsequent wave development despite the periodic initiation. The relationship of these different responses to experimental reaction–diffusion structures reported recently is discussed and the role of the inhibitory species and its spatial profile is revealed.