Abstract
Spiral waves composed of coherent traveling waves surrounding a core containing stochastically distributed stationary areas are found in numerical simulations of a three-variable reaction-diffusion system with one diffusible species. In the spiral core, diffusion of this component (w) mediates transitions between dynamic states of the subsystem formed by the other two components, whose dynamics is more rapid than that of w. Diffusive coupling between adjacent sites can be "on" or "off" depending on the subsystem state. The incoherent structures in the spiral core are produced by this decoupling of the slow diffusive component from the fast non-diffusing subsystem. The phase diagram reveals that the region of incoherent behavior in chimera spirals grows drastically, leading to modulation and breakup of the spirals, in the transition zones between 1(n-1) and 1(n) local mixed-mode oscillations.