Measuring Lyapunov exponents of large chaotic systems with global coupling by time series analysis

被引:3
|
作者
Shimizu, Taro P. [1 ]
Takeuchi, Kazumasa A. [1 ,2 ]
机构
[1] Tokyo Inst Technol, Dept Phys, Meguro Ku, 2-12-1 Ookayama, Tokyo 1528551, Japan
[2] Univ Tokyo, Dept Phys, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, Japan
基金
日本学术振兴会;
关键词
SPECTRUM;
D O I
10.1063/1.5066087
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here, we develop a method to overcome this difficulty, valid for highly symmetric systems such as systems with global coupling, for which the dimensionality of recurrence analysis can be reduced drastically. We test our method numerically with two globally coupled systems, namely, logistic maps and limit-cycle oscillators with global coupling. The evaluated exponent values are successfully compared with the true ones obtained by the standard numerical method. We also describe a few techniques to improve the accuracy of the proposed method. Published by AIP Publishing.
引用
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页数:6
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