Oscillations and waves in the Belousov-Zhabotinskii reaction in a finite medium

Abstract

Travelling reaction-diffusion waves are considered in a finite medium. The model considered is a simplified model of the Belousov-Zhabotinskii reaction, described mathematically by the two-variable Oregonator. A one-dimensional problem consisting of three regions is considered. Regions I (x ⩽ 0) and III (x ⩾ 1) act as reservoirs with fixed concentrations of the reactant X (the autocatalyst, hypobromous acid (HBrO₂)), where the concentration of X in regions I and III may be different. Region II represents a catalyst-loaded membrane, within which species X can diffuse while species Z (the oxidized form of the metal-ion catalyst (Ce(IV))) is fixed spatially. The large time behaviour of the system is considered and both stable steady states and periodic spatio-temporal structures are seen.