Excitable wave patterns in temporal systems with two long delays
2019
Excitable waves arise in many spatially-extended systems of either 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 to interpret them as the result of an effective 2D advection-reaction-diffusion process.
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