Origin of spontaneous wave generation in an oscillatory chemical system

Abstract

The origin of spontaneously generated chemical waves in an oscillatory Belousov-Zhabotinskii reaction has been investigated by numerical calculations of the deterministic reaction-diffusion equations of a modified Oregonator model and by equilibrium stochastic calculations. From numerical calculations, we obtain threshold perturbations in the phase of oscillations and in the concentrations of HBrO{sub 2} and Br{sup {minus}} within areas of space with varying radii necessary to initiate trigger waves. Inward propagating trigger waves initiated by a phase shift in the perturbed region with respect to the bulk solution have been observed in the calculations for the first time. Perturbations smaller than the threshold perturbations or in regions with smaller radii lead to phase-diffusion waves. Our equilibrium stochastic calculations show that the recurrence time for a thermal fluctuation to induce a change in the HBrO{sub 2} concentration of sufficient magnitude within a sufficient volume for a trigger wave to propagate is many orders of magnitude larger than the observation time of traveling wave experiments. We concluded that an internal thermal fluctuation is highly unlikely to generate a trigger wave in an oscillatory chemical solution. 22 refs., 5 figs., 7 tabs.