Creation of spatial structure by an electric field applied to an ionic cubic autocatalator system

Abstract

The effects of applying electric fields to a reactor with kinetics based on an ionic version of the cubic autocatalator are considered. Three types of boundary condition are treated, namely (constant) prescribed concentration, zero flux and periodic. A linear stability analysis is undertaken and this reveals that the conditions for bifurcation from the spatially uniform state are the same for both the prescribed concentration and zero-flux boundary conditions, suggesting bifurcation to steady structures, whereas, for periodic boundary conditions, the bifurcation is essentially different, being of the Hopf type, leading to travelling-wave structures. The various predictions from linear theory are confirmed through extensive numerical simulations of the initial-value problem and by determining solutions to the (non-linear) steady state equations. These reveal, for both prescribed concentration and zero-flux boundary conditions, that applying an electric field can change the basic pattern form, give rise to spatial structure where none would arise without the field, can give multistability and can, if sufficiently strong, suppress spatial structure entirely. For periodic boundary conditions, only travelling waves are found, their speed of propagation and wavelength increasing with increasing field strength, and are found to form no matter how strong the applied field.