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Vortex core dynamics is studied in the Brusselator both near to and far from the Hopf bifurcation line for random and pair initial conditions. Extensive simulations are carried out for a pair of counter-rotating vortices close to the Hopf bifurcation line. Provided the vortices are not so far apart that wave-front annihilation produces strong gradients between their centers, the simulation results compare favorably with theories based on the complex Ginzburg-Landau equation. Far from the Hopf line the vortex core dynamics changes character and phenomena such as periodic motion of the vortex centers arise.

The response of the Brusselator reaction-diffusion system to inhomogeneous perturbations is studied. The main focus of this work is on a spatial generalization of the phase resetting problem. A randomly chosen fraction p of an initially homogeneous oscillatory system is locally perturbed and driven off the limit cycle. The asymptotic local phase is monitored and averaged over local regions and realizations of the perturbation process. From this information a phase response curve can be constructed which depends both on the local stimulus amplitude and on p. The system exhibits two qualitatively different kinds of response depending on the stimulus amplitude and the phase at which the perturbation is applied. It either relaxes to a spatially homogeneous oscillatory state or develops persistent spatial patterns. The origin of this behavior is discussed.

The results of a study of spatial pattern formation in a two-dimensional oscillatory reaction–diffusion system are presented. The calculations are carried out on a discrete model of the Brusselator reaction. The system responds to inhomogeneous perturbations in two different ways. For most perturbations it relaxes back to a spatially homogeneous state with a phase shift. However, special perturbations produce persistent structures which consist of spiral waves and target patterns. The nature of these spatio-temporal states is discussed.