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

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

2003-07-02

arxiv.org/abs/cond-mat/0307057v2

Phys. Rev. Lett. 92, 204101 (2004)

Physics

Condensed Matter

Statistical Mechanics

Final version to appear in Phys. Rev. Lett., 4 pages, 3 eps figs

Scientific paper

10.1103/PhysRevLett.92.204101

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.

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