Abstact
We study the generation of traveling waves in unidirectional chains of coupledoscillators communicating via a phase-dependent pulse-response interaction borrowed from mathematical neuroscience. Preliminary numerical results indicatethe existence of a periodic traveling wave solution as well as the asymptotic relaxation of a single oscillator to the wave when it is forced with the wave generator. Using this evidence as an assumption, we analytically prove global stability of waves in the infinite chain, with respect to initial perturbations offinitely many sites. We conclude with an analytic proof of existence and local stability of traveling wave solutions in a simplified, piecewise-affine interaction model that inherits the main features of the original motivation. In conjunction with the global stability theorem (that holds for a rather general class of models),this latter study proves, in a idealized situation, that families of globally-cstable traveling wave solutions are supported in all parameter regimes.