Excitable wave patterns in temporal systems with two long delays

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.

References in corpus (9)

• Laser Chimeras as a paradigm for multi-stable patterns in complex systems
• Topological solitons as addressable phase bits in a driven laser
• Spatio-temporal phenomena in complex systems with time delays
• Pattern formation in systems with multiple delayed feedbacks
• Arrest of Domain Coarsening via Antiperiodic Regimes in Delay Systems
• Spatio-temporal complexity in dual delay nonlinear laser dynamics: chimeras and dissipative solitons
• Nucleation of reaction-diffusion waves on curved surfaces
• Evidence of a critical phase transition in a purely temporal dynamics with long-delayed feedback
• A new spatio-temporal description of long-delayed systems: ruling the dynamics

Cited by in corpus (7)

• Deep-learning-assisted detection and termination of spiral- and broken-spiral waves in mathematical models for cardiac tissue
• Chaotic Diffusion in Delay Systems: Giant Enhancement by Time Lag Modulation
• Laminar chaos in systems with quasiperiodic delay
• Spatio-temporal representation of long-delayed systems: an alternative approach
• Anti-persistent random walks in time-delayed systems
• Excitability and memory in a time-delayed optoelectronic neuron
• Spiral-wave dynamics in excitable media: Insights from dynamic mode decomposition