We study the existence and stability of propagating fronts in Meinhardt's
reaction-diffusion model of branching in one spatial dimension. We identify a
saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to
episodic front propagation in the parameter region below propagation failure
and show that this state is stable. Stable constant speed fronts exist only
above this parameter value. We use numerical continuation to show that
propagation failure is a consequence of the presence of a T-point corresponding
to the formation of a heteroclinic cycle in a spatial dynamics description.
Additional T-points are identified that are responsible for a large
multiplicity of different traveling front-peak states. The results indicate
that multivariable models may support new types of behavior that are absent
from typical two-variable models but may nevertheless be important in
developmental processes such as branching and somitogenesis.Comment: 18 pages, 12 figure