  We investigate the dynamics of unidirectional semi-infinite chains of type-I
oscillators that are periodically forced at their root node, as an archetype of
wave generation in neural networks. In previous studies, numerical simulations
based on uniform forcing have revealed that trajectories approach a traveling
wave in the far-downstream, large time limit. While this phenomenon seems
typical, it is hardly anticipated because the system does not exhibit any of
the crucial properties employed in available proofs of existence of traveling
waves in lattice dynamical systems. Here, we give a full mathematical proof of
generation under uniform forcing in a simple piecewise affine setting for which
the dynamics can be solved explicitly. In particular, our analysis proves
existence, global stability, and robustness with respect to perturbations of
the forcing, of families of waves with arbitrary period/wave number in some
range, for every value of the parameters in the system.
