A lower-bound estimate of the Lyapunov dimension for the global attractor of the Lorenz system

TL;DR

This paper applies analytical and control techniques to estimate and verify the Lyapunov dimension of the Lorenz attractor, addressing numerical challenges in long-term trajectory analysis.

Contribution

It introduces a combined approach using Pyragas control and Leonov's method for lower-bound Lyapunov dimension estimation of the Lorenz attractor.

Findings

Demonstrates the effectiveness of Pyragas control in the analysis.

Provides a lower-bound estimate consistent with Eden's conjecture.

Discusses numerical methods for finite-time Lyapunov dimension computation.

Abstract

In this short report, for the classical Lorenz attractor we demonstrate the applications of the Pyragas time-delayed feedback control technique and Leonov analytical method for the Lyapunov dimension estimation and verification of the Eden's conjecture. The problem of reliable numerical computation of the finite-time Lyapunov dimension along the trajectories over large time intervals is discussed.