Spatiotemporal representation of long-delayed systems: An alternative approach

Dynamical systems with long-delay feedback can exhibit complicated temporal phenomena, which once reorganized in a two-dimensional space are reminiscent of spatiotemporal behavior. In this framework, a normal forms description has been developed to reproduce the dynamics, and the opportunity to treat the corresponding variables as true space and time has since been established. However, recently, an alternative approach has been proposed [F. Marino and G. Giacomelli, Phys. Rev. E 98, 060201(R) (2018)2470-004510.1103/PhysRevE.98.060201] with a different interpretation of the variables involved, which better takes 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 rethinking of the concept of spatiotemporal representation of long-delayed systems.