Generalised entropy of curves for the analysis and classification of dynamical systems
type: Item
instance of: scholarly article
title: Generalised entropy of curves for the analysis and classification of dynamical systems
zbMATH Open document ID: 1179.37024
author: Andrea Caiti
author: Emanuele Crisostomi
author: Aldo Balestrino
published in: Entropy
publication date: 2010-01-29T00:00:00Z
review text: Summary: This paper provides a new approach for the analysis and eventually the classification of dynamical systems. The objective is pursued by extending the concept of the entropy of plane curves, first introduced within the theory of the thermodynamics of plane curves, to Rn space. Such a generalised entropy of a curve is used to evaluate curves that are obtained by connecting several points in the phase space. As the points change their coordinates according to the equations of a dynamical system, the entropy of the curve connecting them is used to infer the behaviour of the underlying dynamics. According to the proposed method all linear dynamical systems evolve at constant zero entropy, while higher asymptotic values characterise nonlinear systems. The approach proves to be particularly efficient when applied to chaotic systems, in which case it has common features with other classic approaches. Performances of the proposed method are tested over several benchmark problems.
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 5664161
zbMATH Keywords: nonlinear systems
zbMATH Keywords: chaotic systems
zbMATH Keywords: Lyapunov exponents
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e11020249
OpenAlex ID: W2080846230
cites work: A method for nonlinear system classification in the time-frequency plane
cites work: A Lie-Backlund approach to equivalence and flatness of nonlinear systems
cites work: Chaos in Dynamical Systems
cites work: Can one measure the temperature of a curve?
cites work: Using the entropy of curves to segment a time or spatial series
cites work: A Mathematical Theory of Communication
cites work: The Minimum Covering Sphere Problem
cites work: Fast Lyapunov indicators. Application to asteroidal motion
cites work: Detection of ordered and chaotic motion using the dynamical spectra
cites work: Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits
cites work: The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity
cites work: CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
cites work: On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems
cites work: Estimating the Lyapunov exponents of discrete systems
cites work: TIME-VARYING LINEARIZATION AND THE PERRON EFFECTS
cites work: Q4266778
DOI: 10.3390/E11020249
description: scientific article; zbMATH DE number 5664161