Existence and stability of traveling waves in a non-monotone feedforward chain of simple phase oscillators
Stan Mintchev

We consider unidirectional semi-infinite chains of type-I oscillators
periodically forced at their boundary node. In previous studies,
numerical simulations based on uniform-frequency forcing have revealed
that the chain dynamics settles to 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. We will discuss a full
treatment of a simple piecewise-affine setting for which the dynamics
can be solved explicitly. Within this context, we will show how one
may proceed to establish existence, global stability, and robustness
with respect to perturbations of the forcing, of families of waves
with arbitrary period in some range. These results hold for every
value of the parameters in the system; in particular, we will note
that when the coupling is not too strong, the results on robustness
with respect to changes in forcing signal will include the case of
uniform-frequency forcing.