Detecting the unstable periodic orbits of chaotic nonautonomous systems with an approximate global Poincare map

Citation
Yc. Hsiao et Pc. Tung, Detecting the unstable periodic orbits of chaotic nonautonomous systems with an approximate global Poincare map, PHYS LETT A, 290(1-2), 2001, pp. 59-64
Citations number
45
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
PHYSICS LETTERS A
ISSN journal
0375-9601 → ACNP
Volume
290
Issue
1-2
Year of publication
2001
Pages
59 - 64
Database
ISI
SICI code
0375-9601(20011105)290:1-2<59:DTUPOO>2.0.ZU;2-V
Abstract
This Letter presents a simple approach that detects unstable periodic orbit s embedded in a chaotic motion of an unknown nonautonomous system with nois y perturbation. An identification technique is developed to obtain the mode l of the unknown system. The nonautonomous system is approximated by a diff erence system and then a global Poincare map function is derived from the d ifference system. The unstable periodic orbits can be detected via the map function. The proposed method is both accurate and feasible as demonstrated by two chaotic nonautonomous systems. (C) 2001 Published by Elsevier Scien ce B.V.