Numerical evidence of stationary and breathing concentration patterns in the Oregonator with equal diffusivities

The set of three reaction-diffusion equations describing the time-space behavior of the intermediate chemical species in the Oregonator model of the Belousov-Zhabotinsky reaction is investigated in an open, gel-disk reactor in one and two spatial dimensions. Numerical simulations using equal values of the three diffusion coefficients indicate the presence of solutions corresponding to large-amplitude, apparently stable, stationary concentration patterns. The requirement of differential transport rates of chemical activator and inhibitor species for the development of stable patterns is apparently met in this system by differential exchange rates with the reservoir(s) rather than by differential diffusion rates within the gel-reactor. The characteristics of these patterns as well as their stability and bifurcation properties are investigated and suggest that their appearance is dependent upon the existence of bistability in the homogeneous reaction kinetics. The patterns have an intrinsic wavelength, and one of a particular wave-number destabilizes via a Hopf bifurcation as the length of the gel-reactor is varied, giving rise to oscillatory breather-solutions past the bifurcation but before decomposition into a spatially homogeneous state occurs. The relationship of these results to experimental systems, as well as an analogy to the behavior of biological membranes, is discussed.