Statistical Versus Optimal Partitioning For Block Entropies

Abstract

Purpose: Given A Time-Series, What Is The Best Partitioning Of The State Space In Order To Obtain Reasonable Values For The Block Entropies? The Purpose Of This Paper Is To Provide A Simple Answer (An Algorithm), Although Approximative, In Connection With Symbolic Dynamics And Statistical Properties Of 1-D Maps On The Interval. Design/methodology/approach: The Logistic Map Is Examined As An Archetype Of A Complex System With Different Behaviors, Namely: Periodicity, Order-To-Chaos Period-Doubling Transition, Weak Chaos, Parametric Intermittent Chaos, Developed Chaos And Fully Developed Chaos. For The Logistic Map The Generating Partition Is Known, And Allows Comparison With Other Prescriptions In The Literature. The Partitioning Of The Phase Space With The Easy Generated Bipartition Induced By The Mean Value Of A Curve In The Plane, Gives Results In Good Agreement (Roughly Up To A 20 Per Cent Difference) With The Results Of The Generating Partition, If The Trajectory Of The System Is In Parametric Intermittent Chaos And In Developed Chaos (DC). In The Case Of Fully Developed Chaos (FDC), The Agreement Is Perfect. Findings: The Authors Confirm That A Statistical Partitioning Is Almost Equivalent With The Exact Partitioning For The Logistic Map. Originality/value: The Paper Updates Previous Results And Proposes A Better Understanding On The Partitioning For Symbolic Dynamics. © Emerald Group Publishing Limited.

Department(s)

Physics

Keywords and Phrases

Block entropies; Dynamical systems; Dynamics; Lumping; Symbolic dynamics; Time series analysis

International Standard Serial Number (ISSN)

0368-492X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Emerald, All rights reserved.

Publication Date

01 Jan 2013

Link to Full Text

Share

 
COinS