Burning lobes in an advection-reaction-diffusion system

We use the tools developed for chaotic fluid transport to describe the propagation of a reaction front in a chain of oscillating vortices. Specifically, we expand the concept of lobes (turnstiles) bounded by stable and unstable manifolds to account for the propagation of a reaction front. A ``burning lobe'' is a passive lobe that grows due to the reactive medium. We propose that a reaction front will propagate from one vortex to the next in an oscillation period if a portion of the front was within the burning lobe. This framework is used to explain mode-locking of reaction fronts propagating in an oscillating vortex array.