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

Alejandro D. Sanchez·Juan M. Lopez·Miguel A. Rodriguez·Manuel A. Matias
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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.

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BibTeXRIS

Alejandro D. Sanchez, Juan M. Lopez, Miguel A. Rodriguez, Manuel A. Matias. 2004-03-30. Rare Events and Scale--Invariant Dynamics of Perturbations in Delayed Dynamical Systems. https://doi.org/10.1103/physrevlett.92.204101

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