Relationship between delayed and spatially extended dynamical systems

The interpretation of delayed dynamical systems (DDS) in terms of a suitable spatiotemporal dynamics is put on a rigorous ground by deriving amplitude equations in the vicinity of a Hopf bifurcation. We show that comoving Lyapunov exponents can be defined and computed in a DDS. From the propagation of localized infinitesimal disturbances in DDS, we show the existence of convective type instabilities. Moreover, a widely studied class of DDS is mapped onto an evolution rule fur a spatial system with drift and diffusion.