Efficient algorithm for detecting unstable periodic orbits in chaotic systems

被引：72

作者：

Davidchack, RL ^{[1
]}

Lai, YC

机构：

[1] Univ Kansas, Dept Phys & Astron, Lawrence, KS 66045 USA

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

PHYSICAL REVIEW E | 1999年 / 60卷 / 05期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1103/PhysRevE.60.6172

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We present an efficient method for Fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of an 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. [S1063-651X(99)06711-2].

引用

页码：6172 / 6175

页数：4

共 17 条

[1] EXPLORING CHAOTIC MOTION THROUGH PERIODIC-ORBITS [J].

AUERBACH, D ;

CVITANOVIC, P ;

ECKMANN, JP ;

GUNARATNE, G ;

PROCACCIA, I .

PHYSICAL REVIEW LETTERS, 1987, 58 (23) :2387-2389

[2] CHARACTERIZATION OF UNSTABLE PERIODIC-ORBITS IN CHAOTIC ATTRACTORS AND REPELLERS [J].

BIHAM, O ;

WENZEL, W .

PHYSICAL REVIEW LETTERS, 1989, 63 (08) :819-822

[3] CONTROLLING NONCHAOTIC NEURONAL NOISE USING CHAOS CONTROL TECHNIQUES [J].

CHRISTINI, DJ ;

COLLINS, JJ .

PHYSICAL REVIEW LETTERS, 1995, 75 (14) :2782-2785

[4] Systematic computation of the least unstable periodic orbits in chaotic attractors [J].

Diakonos, FK ;

Schmelcher, P ;

Biham, O .

PHYSICAL REVIEW LETTERS, 1998, 81 (20) :4349-4352

[5] UNSTABLE PERIODIC-ORBITS AND THE DIMENSIONS OF MULTIFRACTAL CHAOTIC ATTRACTORS [J].

GREBOGI, C ;

OTT, E ;

YORKE, JA .

PHYSICAL REVIEW A, 1988, 37 (05) :1711-1724

[6]

Gutzwiller MC, 1990, CHAOS CLASSICAL QUAN

[7] ALTERNATIVE METHOD TO FIND ORBITS IN CHAOTIC SYSTEMS [J].

HANSEN, KT .

PHYSICAL REVIEW E, 1995, 52 (03) :2388-2391

[8] Optimal periodic orbits of chaotic systems [J].

Hunt, BR ;

Ott, E .

PHYSICAL REVIEW LETTERS, 1996, 76 (13) :2254-2257

[9] MULTIPLE-VALUED STATIONARY STATE AND ITS INSTABILITY OF THE TRANSMITTED LIGHT BY A RING CAVITY SYSTEM [J].

IKEDA, K .

OPTICS COMMUNICATIONS, 1979, 30 (02) :257-261

[10] Characterization of the natural measure by unstable periodic orbits in chaotic attractors [J].

Lai, YC ;

Nagai, Y ;

Grebogi, C .

PHYSICAL REVIEW LETTERS, 1997, 79 (04) :649-652

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