The initiation and propagation of travelling waves on membrane interfaces in the Belousov-Zhabotinskii reaction

Abstract

Travelling reaction-diffusion waves are considered in a simplified model of the Belousov -Zhabotinskii reaction, described mathematically by the two-variable Oregonator. A one-dimensional problem consisting of two regions is considered. Region I (effectively the boundary at x ' = 0) acts as a reservoir with a fixed concentration of the autocatalytic species (hypobromous acid), and provides constant in put of this species in to region II. Region II (the reaction zone 0 < x & < ∞) allows diffusion of the autocatalyst while the catalytic species Ce IV is assumed immobilized on a supporting matrix . The form of the ensuing travelling wavefront and the behaviour in the behind the front as it propagates in to the region of increasing x ', is considered. By examining the large time behaviour it is shown that the propagating front travels with its minimum possible wave speed. Both single travelling waves and periodic wave trains are observed.