Electric field effects on travelling waves in the Oregonator model for the Belousov-Zhabotinsky reaction

The effects of an electric field on the travelling waves arising in Belousov-Zhabotinsky systems are analysed using the Oregonator to describe the kinetics. The model is reduced to a two-variable version involving the concentrations of HBrO2 and M-ox(3+), the oxidized form of the catalyst, using previously-suggested scalings. The travelling wave equations for this two-variable model are solved numerically for a range of kinetic parameters and the ratio of diffusion coefficients D. An upper bound on the field strength E is found, arising from a saddle-node bifurcation, for the existence of travelling waves. There can also be a lower bound on E for their existence, dependent on the other parameters in the system. The conditions for this termination of a solution at a finite field strength are determined. In other cases, travelling waves exist for all negative field strengths and an asymptotic solution for large \E\ is constructed. This acts as a confirmation of the numerical results and provides further insights into the structure of the wave profiles. Numerical integrations of the corresponding initial-value problem are undertaken. These show wave deceleration and annihilation in positive fields and wave acceleration in negative fields, in line with experimental observations. In cases when there is termination at a finite value of E, wave trains are seen to develop for (negative) field strength less than this value.