Structure of characteristic Lyapunov vectors in spatiotemporal chaos

TL;DR

This paper investigates the structure of characteristic Lyapunov vectors in spatiotemporal chaos, revealing universal features across different systems and proposing a stochastic model to replicate these properties.

Contribution

It compares characteristic and backward Lyapunov vectors across diverse chaotic systems and introduces a minimal stochastic model demonstrating universality.

Findings

Characteristic Lyapunov vectors exhibit universal features across systems.

A stochastic model reproduces the observed Lyapunov vector structures.

Results support earlier claims of universality in spatiotemporal chaos.

Abstract

We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in systems with spatiotemporal chaos. We focus on characteristic LVs and compare the results with backward LVs obtained via successive Gram-Schmidt orthonormalizations. Systems of a very different nature such as coupled-map lattices and the (continuous-time) Lorenz `96 model exhibit the same features in quantitative and qualitative terms. Additionally we propose a minimal stochastic model that reproduces the results for chaotic systems. Our work supports the claims about universality of our earlier results [I. G. Szendro et al., Phys. Rev. E 76, 025202(R) (2007)] for a specific coupled-map lattice.