TRANSITION FROM PHASE WAVES TO TRIGGER WAVES IN A MODEL OF THE ZHABOTINSKII REACTION

In principle, two kinds of traveling waves of chemical activity may occur during the ferroin-catalyzed oxidation of malonic acid by bromate ion. The first of these, called a phase wave, propagates independently of diffusion along a phase gradient in an oscillatory reagent. The second of these, called a trigger wave, propagates by means of the interaction of chemical reaction and diffusion of intermediate species in an excitable reagent. An oscillatory reagent is also excitable. A model of the chemistry occurring in this reaction has been proposed. It is shown here that the partial differential equations describing the dynamics of the interaction of reaction and diffusion in this model possess solutions corresponding to both phase waves and trigger waves. These equations are solved numerically using a finite difference implementation of the method of lines. Our results show that phase waves appear only in an oscillatory reagent and travel at a velocity equal to the reciprocal of the phase gradient which they are propagating along. The range of possible phase wave velocities in a particular reagent is very large. Trigger waves appear in either an oscillatory or merely excitable reagent. In a nonoscillatory, but excitable, reagent they travel at a unique velocity defined by the reactive and diffusive properties of the system. In an oscillatory reagent, trigger wave velocity may be variable as a result of spatial gradients in bromide ion concentration residual from an initially present phase gradient. If a phase wave is moving more slowly than a trigger wave would move under the same conditions, then the phase wave will initiate this trigger wave. Calculated trigger wave velocities agree satisfactorily with the observed value. © 1979, American Chemical Society. All rights reserved.