Characteristic Lyapunov vectors in chaotic time-delayed systems

TL;DR

This paper analyzes Lyapunov vectors in chaotic delay-differential systems, revealing long-range correlations and universality class behavior similar to dissipative spatiotemporal chaos, especially in large delay limits.

Contribution

It demonstrates that characteristic Lyapunov vectors in large delay systems exhibit long-range correlations and belong to the KPZ universality class, linking delay systems to spatiotemporal chaos.

Findings

Lyapunov vectors show long-range correlations

Characteristic LVs belong to KPZ universality class

Large delay systems behave like dissipative spatiotemporal chaos

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.