  Fronts propagating in two-dimensional advection-reaction-diffusion (ARD)
systems exhibit rich topological structure. When the underlying fluid flow is
periodic in space and time, the reaction front can lock to the driving
frequency. We explain this mode-locking phenomenon using so-called burning
invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a
BIM attached to a relative periodic orbit (RPO) of the front element dynamics.
Changes in the type (and loss) of mode-locking can be understood in terms of
local and global bifurcations of the RPOs and their BIMs. We illustrate these
concepts numerically using a chain of alternating vortices in a channel
geometry.
