Efficient algorithm for detecting unstable periodic orbits in chaotic systems
chao-dyn
2009-10-31 v1 Chaotic Dynamics
Abstract
We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has both fast and global convergence, and only a small number of initial points is sufficient to detect all unstable periodic orbits of a given period. The power of our method is illustrated by numerical examples of both two- and four-dimensional maps.
Cite
@article{arxiv.chao-dyn/9906007,
title = {Efficient algorithm for detecting unstable periodic orbits in chaotic systems},
author = {Ruslan L. Davidchack and Ying-Cheng Lai},
journal= {arXiv preprint arXiv:chao-dyn/9906007},
year = {2009}
}
Comments
4 pages, 3 figures, 1 table, submitted to PRE as Rapid Communication