Excitable Wave Patterns in Temporal Systems with Two Long Delays and their Observation in a Semiconductor Laser Experiment

Excitable waves arise in many spatially extended systems of either a biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the time dynamics of an excitable system with two, hierarchically long delays. The transition from 1D localized structures to curved wave segments is experimentally observed in an excitable semiconductor laser with two feedback loops and reproduced by numerical simulations of a prototypical model. While closely related to those found in 2D excitable media, wave patterns in delayed systems exhibit unobserved features originating from causality related constraints. An appropriate dynamical representation of the data uncovers these phenomena and permits us to interpret them as the result of an effective 2D advection-reaction-diffusion process.