Reconstructing bifurcation diagrams with Lyapunov exponents from only time-series data using an extreme learning machine
Reconstructing bifurcation diagrams with Lyapunov exponents from only time-series data using an extreme learning machine
复制标题
使用极限学习机仅根据时间序列数据用李亚普诺夫指数重建分岔图
DOI：
10.1587/nolta.8.2
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
M. Adachi
中科院分区：
文献类型：
--
作者：
Y. Itoh;Y. Tada;M. Adachi
本文描述了一种仅使用时间序列数据重建混沌系统的李雅普诺夫指数分岔图的方法。分岔图的重构是一个时间序列预测问题，用于预测参数变化时时间序列数据的振荡模式。因此，我们期望分岔图的重建可以用于具有可变环境因素（如温度、压力和浓度）的现实世界系统。在传统的方法中，只能定性地评价重建的准确性。本文对重构的分岔图估计了Lyapunov指数，从而定量地评价了重构的结果。我们还给出了数值实验结果，证实了重建的分岔图的特征与原始分岔图的特征一致。
We describe a method for reconstructing bifurcation diagrams with Lyapunov exponents for chaotic systems using only time-series data. The reconstruction of bifurcation diagrams is a problem of time-series prediction and predicts oscillatory patterns of time-series data when parameters change. Therefore, we expect the reconstruction of bifurcation diagram could be used for real-world systems that have variable environmental factors, such as temperature, pressure, and concentration. In the conventional method, the accuracy of the reconstruction can be evaluated only qualitatively. In this paper, we estimate Lyapunov exponents for reconstructed bifurcation diagrams so that we can quantitatively evaluate the reconstruction. We also present the results of numerical experiments that confirm that the features of the reconstructed bifurcation diagrams coincide with those of the original ones.