Cubic autocatalysis in a reaction–diffusion annulus: semi-analytical solutions

Abstract

Semi-analytical solutions for cubic autocatalytic reactions are considered in a circularly symmetric reaction–diffusion annulus. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations and analyzed to obtain semi-analytical results for this novel geometry. Singularity theory is used to determine the regions of parameter space in which the different types of steady-state diagram occur. The region of parameter space, in which Hopf bifurcations can occur, is found using a degenerate Hopf bifurcation analysis. A novel feat..