Compressing phase space detects state changes in nonlinear dynamical systems

TL;DR

This paper introduces a novel method using lossless compression of time series data to accurately reconstruct nonlinear system dynamics, detect state changes, and measure complexity efficiently, even with short sequences.

Contribution

It proposes a new approach that leverages lossless compression for optimal phase space reconstruction and state change detection in nonlinear dynamical systems.

Findings

Detects system state changes such as weak synchronization.

Provides a measure of complexity from short sequences.

Integrates Lyapunov and fractal analysis results.

Abstract

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences to be accurate. In this paper, we show that an optimal reconstruction can be achieved by lossless compression of system's time course, providing a self-consistent analysis of its dynamics and a measure of its complexity, even for short sequences. Our measure of complexity detects system's state changes such as weak synchronization phenomena, characterizing many systems, in one step, integrating results from Lyapunov and fractal analysis.