A database of rigorous and high-precision periodic orbits of the Lorenz model

Roberto Barrio, Angeles Dena, Warwick Tucker

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)

Abstract

A benchmark database of very high-precision numerical and validated initial conditions of periodic orbits for the Lorenz model is presented. This database is a "computational challenge" and it provides the initial conditions of all periodic orbits of the Lorenz model up to multiplicity 10 and guarantees their existence via computer-assisted proofs methods. The orbits are computed using high-precision arithmetic and mixing several techniques resulting in 1000 digits of precision on the initial conditions of the periodic orbits, and intervals of size 10100 that prove the existence of each orbit. Program summary Program title: Lorenz-Database Catalogue identifier: AEWM-v1-0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWM-v1-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 8515 No. of bytes in distributed program, including test data, etc.: 6964501 Distribution format: tar.gz Programming language: Data. Computer: Any computer. Operating system: Any. RAM: Database, no requirements Classification: 4.3, 4.12. Nature of problem: Database of all periodic orbits of the Lorenz model up to multiplicity 10 with 1000 precision digits. Solution method: Advanced search methods for locating unstable periodic orbits combined with the Taylor series method for multiple precision integration of ODEs and interval methods for providing Computer-Assisted proofs of the periodic orbits. Unusual features: The database gives 100 digits rigorously proved using Computer-Assisted techniques and 1000 digits using an optimal adaptive Taylor series method. Running time: Not Applicable.

Original languageEnglish
Pages (from-to)76-83
Number of pages8
JournalComputer Physics Communications
Volume194
DOIs
Publication statusPublished - Sep 2015
Externally publishedYes

Keywords

  • Computer-assisted proof
  • High-precision
  • Lorenz model
  • Periodic orbits
  • Validated numerics

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