arXiv:2611.13832v1 Announce Type: new Abstract: This article investigates the existence and stability of periodic behavior arising in the feedback interconnection of neuromorphic systems, which evolve according to continuous dynamics but interact only through discrete events. Exploiting the event-driven nature of this interaction, each system is modeled by an operator that maps the history of events to the delay of its response. Building on the fading-memory properties of these operators, the article develops a small-gain result establishing the existence, uniqueness, and robustness of periodic one-to-one rhythms.