Predictability: a way to characterize complexity

2001/01/17 by G. Boffetta, M. Cencini, M. Falcioni +1 · 4 citations
Economics, Econometrics and Finance · Environmental Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Chaotic #Characterization (materials science) #Complex Systems and Time Series Analysis #Complex system #Computer science #Dynamical systems theory #Ecosystem dynamics and resilience #Entropy (arrow of time) #Ergodic theory #Generalization #Information theory #Kolmogorov complexity #Lyapunov exponent #Mathematics #Phase space #Physics #Predictability #Pure mathematics #Randomness #Statistical Mechanics and Entropy #Statistical physics #Theoretical computer science #cond-mat #nlin.CD

paper · pdf · doi:10.1016/s0370-1573(01)00025-4

published as Physics Reports 356, 367-474 (2002) · 142 Latex pgs. 41 included eps figures, submitted to Physics Reports. Related information at this http://axtnt2.phys.uniroma1.it

arxiv created 2001/01/17 · openalex publication_date 2002/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a characterization of the unpredictability of a system gives a measure of its complexity. Adopting this point of view, we review some developments in the characterization of the predictability of systems showing different kind of complexity: from low-dimensional systems to high-dimensional ones with spatio-temporal chaos and to fully developed turbulence. A special attention is devoted to finite-time and finite-resolution effects on predictability, which can be accounted with suitable generalization of the standard indicators. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system. The characterization of irregular behavior in systems with discrete phase space is also considered.

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Cited by

• Prediction of chaotic dynamics from data: An introduction
• Stability measures in metastable states with Gaussian colored noise
• On finite-size Lyapunov exponents in multiscale systems
• Flow networks: A characterization of geophysical fluid transport