作者
Tyrus Berry, John Robert Cressman, Zrinka Greguric-Ferencek, Timothy Sauer
发表日期
2013
期刊
SIAM Journal on Applied Dynamical Systems
卷号
12
期号
2
页码范围
618-649
出版商
Society for Industrial and Applied Mathematics
简介
It has long been known that the method of time-delay embedding can be used to reconstruct nonlinear dynamics from time series data. A less-appreciated fact is that the induced geometry of time-delay coordinates increasingly biases the reconstruction toward the stable directions as delays are added. This bias can be exploited, using the diffusion maps approach to dimension reduction, to extract dynamics on desired time scales from high-dimensional observed data. We demonstrate the technique on a wide range of examples, including data generated by a model of meandering spiral waves and video recordings of a liquid-crystal experiment.
学术搜索中的文章
T Berry, JR Cressman, Z Greguric-Ferencek, T Sauer - SIAM Journal on Applied Dynamical Systems, 2013