Rare Events and Scale-Invariant Dynamics of Perturbations in Delayed Chaotic Systems

We study the dynamics of perturbations in time delayed dynamical systems. Using a suitable space-time coordinate transformation, we find that the time evolution of the linearized perturbations (Lyapunov vector) can be mapped to the linear Zhang surface growth model [Y.-C. Zhang, J. Phys. France 51, 5129 (1990)], which is known to describe surface roughening driven by power-law distributed noise. As a consequence, Lyapunov vector dynamics is dominated by rare random events that lead to non-Gaussian fluctuations and multiscaling properties.