Efficient algorithm for detecting unstable periodic orbits in chaotic systems

Citation
Rl. Davidchack et Yc. Lai, Efficient algorithm for detecting unstable periodic orbits in chaotic systems, PHYS REV E, 60(5), 1999, pp. 6172-6175
Citations number
17
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW E
ISSN journal
1063651X → ACNP
Volume
60
Issue
5
Year of publication
1999
Part
B
Pages
6172 - 6175
Database
ISI
SICI code
1063-651X(199911)60:5<6172:EAFDUP>2.0.ZU;2-7
Abstract
We present an efficient method for Fast, complete, and accurate detection o f unstable periodic orbits in chaotic systems. Our method consists of an it erative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has bot h 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 p ower of our method is illustrated by numerical examples of both two- and fo ur-dimensional maps. [S1063-651X(99)06711-2].