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arXiv · 1101.2779

Characteristic Lyapunov vectors in chaotic time-delayed systems

Diego Pazó·Juan M. López
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Abstract

We compute Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in delay-differential equations with large time delay. We find that characteristic LVs, and backward (Gram-Schmidt) LVs, exhibit long-range correlations, identical to those already observed in dissipative extended systems. In addition we give numerical and theoretical support to the hypothesis that the main LV belongs, under a suitable transformation, to the universality class of the Kardar-Parisi-Zhang equation. These facts indicate that in the large delay limit (an important class of) delayed equations behave exactly as dissipative systems with spatiotemporal chaos.

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Diego Pazó, Juan M. López. 2011-01-14. Characteristic Lyapunov vectors in chaotic time-delayed systems. https://doi.org/10.1103/physreve.82.056201

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