Next Article in Journal
The Topological Pressure of Linear Cellular Automata
Previous Article in Journal
Particle Indistinguishability Symmetry within a Field Theory. Entropic Effects
Article Menu

Article Versions

Export Article

Open AccessArticle
Entropy 2009, 11(2), 249-270; doi:10.3390/e11020249

Generalised Entropy of Curves for the Analysis and Classification of Dynamical Systems

Department of Electrical Systems and Automation, University of Pisa, Via Diotisalvi 2, 56100, Pisa, Italy
*
Author to whom correspondence should be addressed.
Received: 12 January 2009 / Accepted: 24 April 2009 / Published: 29 April 2009
View Full-Text   |   Download PDF [1740 KB, uploaded 24 February 2015]   |  

Abstract

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. View Full-Text
Keywords: nonlinear systems; chaotic systems; Lyapunov exponents nonlinear systems; chaotic systems; Lyapunov exponents
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Balestrino, A.; Caiti, A.; Crisostomi, E. Generalised Entropy of Curves for the Analysis and Classification of Dynamical Systems. Entropy 2009, 11, 249-270.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top