English

Excitable wave patterns in temporal systems with two long delays

Pattern Formation and Solitons 2019-05-08 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1901.04383,
  title  = {Excitable wave patterns in temporal systems with two long delays},
  author = {Francesco Marino and Giovanni Giacomelli},
  journal= {arXiv preprint arXiv:1901.04383},
  year   = {2019}
}
R2 v1 2026-06-23T07:11:12.211Z