Inhomogeneous perturbations and phase resetting in an oscillatory reaction–diffusion system

Abstract

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.