Spatio-temporal representation of long-delayed systems: an alternative approach

Abstract

Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been developed to reproduce the dynamics and the opportunity to treat the corresponding variables as true space and time has been since established. However, recently an alternative approach has been proposed in Ref. \cite{Marino2018} with a different interpretation of the variables involved, which takes better into account their physical character and allows for an easier determination of the normal forms. In this paper, we extend such idea and apply it to a number of paradigmatic examples, paving the way to a re-thinking of the concept of spatio-temporal representation of long-delayed systems.

References in corpus (4)

• 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
• Excitable wave patterns in temporal systems with two long delays

Cited by in corpus (5)

• Chaotic Diffusion in Delay Systems: Giant Enhancement by Time Lag Modulation
• Laminar chaos in systems with quasiperiodic delay
• Anti-persistent random walks in time-delayed systems
• Influence of time-delayed feedback on the dynamics of temporal localized structures in passively mode-locked semiconductor lasers
• Impact of phase modulation on the dynamics of temporal localized structures in injected Kerr microcavities