Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems

Zbigniew Galias; Warwick Tucker

doi:10.1109/ISCAS.2009.5118153

Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

Abstract

It is shown that the problem of existence of periodic orbits can be studied rigorously by means of a symbolic dynamics approach combined with interval methods. Symbolic dynamics is used to find approximate initial positions of periodic points and interval operators are used to prove the existence of periodic orbits in a neighborhood of the computer generated solution. As an example the Lorenz system is studied. All 2536 periodic orbits of the Poincaré map with the period n ≤ 14 are found.

Original language	English
Title of host publication	2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009
Pages	1907-1910
Number of pages	4
DOIs	https://doi.org/10.1109/ISCAS.2009.5118153
Publication status	Published - 26 Oct 2009
Externally published	Yes
Event	2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009 - Taipei, Taiwan Duration: 24 May 2009 → 27 May 2009

Publication series

Name	Proceedings - IEEE International Symposium on Circuits and Systems
ISSN (Print)	0271-4310

Conference

Conference	2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009
Country	Taiwan
City	Taipei
Period	24/05/09 → 27/05/09

Access to Document

10.1109/ISCAS.2009.5118153

Link to publication in Scopus

Cite this

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title = "Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems",

abstract = "It is shown that the problem of existence of periodic orbits can be studied rigorously by means of a symbolic dynamics approach combined with interval methods. Symbolic dynamics is used to find approximate initial positions of periodic points and interval operators are used to prove the existence of periodic orbits in a neighborhood of the computer generated solution. As an example the Lorenz system is studied. All 2536 periodic orbits of the Poincar{\'e} map with the period n ≤ 14 are found.",

author = "Zbigniew Galias and Warwick Tucker",

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doi = "10.1109/ISCAS.2009.5118153",

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series = "Proceedings - IEEE International Symposium on Circuits and Systems",

pages = "1907--1910",

booktitle = "2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009",

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Galias, Z & Tucker, W 2009, Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems. in 2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009. Proceedings - IEEE International Symposium on Circuits and Systems, pp. 1907-1910, 2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009, Taipei, Taiwan, 24/05/09. https://doi.org/10.1109/ISCAS.2009.5118153

Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems. / Galias, Zbigniew; Tucker, Warwick.

2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009. 2009. p. 1907-1910 (Proceedings - IEEE International Symposium on Circuits and Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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