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A database of rigorous and high-precision periodic orbits of the Lorenz model
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2015 (English)In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 194, 76-83 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2015. Vol. 194, 76-83 p.
Keyword [en]
Computer-assisted proof, Periodic orbits, Validated numerics, High-precision, Lorenz model
National Category
Computer Science
URN: urn:nbn:se:uu:diva-257618DOI: 10.1016/j.cpc.2015.04.007ISI: 000356196000009OAI: oai:DiVA.org:uu-257618DiVA: diva2:840597
Swedish Research Council, 2007-523
Available from: 2015-07-08 Created: 2015-07-06 Last updated: 2016-02-17Bibliographically approved

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