Compressing Phase Space Detects State Changes in Nonlinear Dynamical Systems. (22nd July 2020)

• Record Type: Journal Article
• Authors: d'Andrea, Valeria; De Domenico, Manlio
• Other Names: Messias Marcelo Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-07-22
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/8650742
• Languages: English
• ISSNs: 1076-2787

Abstract

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.