# Uncovering low dimensional macroscopic chaotic dynamics of large finite size complex systems

## TL;DR

This paper demonstrates that techniques for analyzing noisy chaotic time series can identify low-dimensional macroscopic chaotic dynamics in large finite systems, exemplified by globally coupled Landau-Stuart oscillators.

## Contribution

It introduces a novel approach to uncover low-dimensional macroscopic chaos in finite systems using time series analysis techniques originally designed for noisy experimental data.

## Key findings

- Successfully identified 4-dimensional macroscopic chaos in coupled oscillators
- Calculated dynamical invariants like Lyapunov exponents and attractor dimensions
- Enabled short-term predictions of the system's macroscopic behavior

## Abstract

In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the macroscopic dynamics of other similar systems also have a low dimensional description in the infinite N limit has, however, remained elusive. In this paper we show how techniques originally designed to analyze noisy experimental chaotic time series can be used to identify effective low dimensional macroscopic descriptions from simulations with a finite number of elements. We illustrate and verify the effectiveness of our approach by applying it to the dynamics of an ensemble of globally coupled Landau-Stuart oscillators for which we demonstrate low dimensional macroscopic chaotic behavior with an effective 4-dimensional description. By using this description we show that one can calculate dynamical invariants such as Lyapunov exponents and attractor dimensions. One could also use the reconstruction to generate short-term predictions of the macroscopic dynamics.