Scytale decodes chaos: A method for estimating unstable symmetric solutions

Yasuaki Morita; Naoya Fujiwara; Miki U. Kobayashi; Tsuyoshi Mizuguchi

doi:10.1063/1.3365053

Scytale decodes chaos: A method for estimating unstable symmetric solutions

Yasuaki Morita, Naoya Fujiwara, Miki U. Kobayashi, Tsuyoshi Mizuguchi

INF - Human-Social Information Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

A method for estimating a period of unstable periodic solutions is suggested in continuous dissipative chaotic dynamical systems. The measurement of a minimum distance between a reference state and an image of transformation of it exhibits a characteristic structure of the system, and the local minima of the structure give candidates of period and state of corresponding symmetric solutions. Appropriate periods and initial states for the Newton method are chosen efficiently by setting a threshold to the range of the minimum distance and the period.

Original language	English
Article number	031001CHA
Journal	Chaos
Volume	20
Issue number	1
DOIs	https://doi.org/10.1063/1.3365053
Publication status	Published - 2010 Mar

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

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title = "Scytale decodes chaos: A method for estimating unstable symmetric solutions",

abstract = "A method for estimating a period of unstable periodic solutions is suggested in continuous dissipative chaotic dynamical systems. The measurement of a minimum distance between a reference state and an image of transformation of it exhibits a characteristic structure of the system, and the local minima of the structure give candidates of period and state of corresponding symmetric solutions. Appropriate periods and initial states for the Newton method are chosen efficiently by setting a threshold to the range of the minimum distance and the period.",

author = "Yasuaki Morita and Naoya Fujiwara and Kobayashi, {Miki U.} and Tsuyoshi Mizuguchi",

note = "Funding Information: The authors thank Professor Fujisaka, Professor Daido, Professor Horita, Dr. Saiki, Professor Pikovsky, Professor Iba, Professor Nishiura, Professor Iima, Professor Tanaka, and Professor Watanabe for valuable discussions and comments. This work is supported by JST PRESTO program. One of the authors (N.F.) is supported by SFB 555 (DFG). M.U.K. is supported by a Grant-in-Aid for JSPS Fellows. The numerical calculations were performed partly at YITP at Kyoto University.",

year = "2010",

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doi = "10.1063/1.3365053",

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AU - Mizuguchi, Tsuyoshi

N1 - Funding Information: The authors thank Professor Fujisaka, Professor Daido, Professor Horita, Dr. Saiki, Professor Pikovsky, Professor Iba, Professor Nishiura, Professor Iima, Professor Tanaka, and Professor Watanabe for valuable discussions and comments. This work is supported by JST PRESTO program. One of the authors (N.F.) is supported by SFB 555 (DFG). M.U.K. is supported by a Grant-in-Aid for JSPS Fellows. The numerical calculations were performed partly at YITP at Kyoto University.

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Scytale decodes chaos: A method for estimating unstable symmetric solutions

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