Rare Events and Scale--Invariant Dynamics of Perturbations in Delayed Dynamical Systems
Statistical Mechanics
2009-11-10 v2 Chaotic Dynamics
Abstract
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 {\bf 51}, 2129 (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.
Keywords
Cite
@article{arxiv.cond-mat/0307057,
title = {Rare Events and Scale--Invariant Dynamics of Perturbations in Delayed Dynamical Systems},
author = {Alejandro D. Sanchez and Juan M. Lopez and Miguel A. Rodriguez and Manuel A. Matias},
journal= {arXiv preprint arXiv:cond-mat/0307057},
year = {2009}
}
Comments
Final version to appear in Phys. Rev. Lett., 4 pages, 3 eps figs