Characteristic Lyapunov vectors in chaotic time-delayed systems

Details Characteristic Lyapunov vectors in chaotic time-delayed systems Characteristic Lyapunov vectors in chaotic time-delayed systems

2011-01-14

arxiv.org/abs/1101.2779v1

Phys. Rev. E 82, 056201 (2010)

Nonlinear Sciences

Chaotic Dynamics

7 pages

Scientific paper

10.1103/PhysRevE.82.056201

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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