Scytale decodes chaos: A method for estimating unstable symmetric solutions

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

doi:10.1063/1.3365053

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.

ACKNOWLEDGMENTS

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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