Transition from strange nonchaotic to strange chaotic attractors

Research output: Contribution to journalArticle

66 Citations (Scopus)

Abstract

We investigate the transition from strange nonchaotic to strange chaotic attractors in quasiperiodically driven dynamical systems. It is found that whether the asymptotic attractor of the system is strange nonchaotic or strange chaotic is determined by the relative weight of the contraction and expansion for infinitesimal vectors along a typical trajectory on the attractor. When the average contraction dominates the average expansion, the attractor is strange nonchaotic. Strange chaotic attractors arise when the average expansion dominates the average contraction. The transition from strange nonchaotic to strange chaotic attractors occurs when the average contraction and expansion are balanced. A characteristic signature of this route to chaos is that the Lyapunov exponent passes through zero linearly. We provide numerical confirmation using both a quasiperiodically driven map and a quasiperiodic flow.

Original languageEnglish (US)
Pages (from-to)57-65
Number of pages9
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume53
Issue number1 SUPPL. A
StatePublished - 1996
Externally publishedYes

Fingerprint

Strange attractor
Chaotic Attractor
contraction
Contraction
Attractor
expansion
strange attractors
Lyapunov Exponent
dynamical systems
chaos
Chaos
Signature
Linearly
Dynamical system
routes
signatures
trajectories
exponents
Trajectory
Zero

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

@article{9e9c45a1df2048ce9e27495839e35b11,
title = "Transition from strange nonchaotic to strange chaotic attractors",
abstract = "We investigate the transition from strange nonchaotic to strange chaotic attractors in quasiperiodically driven dynamical systems. It is found that whether the asymptotic attractor of the system is strange nonchaotic or strange chaotic is determined by the relative weight of the contraction and expansion for infinitesimal vectors along a typical trajectory on the attractor. When the average contraction dominates the average expansion, the attractor is strange nonchaotic. Strange chaotic attractors arise when the average expansion dominates the average contraction. The transition from strange nonchaotic to strange chaotic attractors occurs when the average contraction and expansion are balanced. A characteristic signature of this route to chaos is that the Lyapunov exponent passes through zero linearly. We provide numerical confirmation using both a quasiperiodically driven map and a quasiperiodic flow.",
author = "Ying-Cheng Lai",
year = "1996",
language = "English (US)",
volume = "53",
pages = "57--65",
journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",
number = "1 SUPPL. A",

}

TY - JOUR

T1 - Transition from strange nonchaotic to strange chaotic attractors

AU - Lai, Ying-Cheng

PY - 1996

Y1 - 1996

N2 - We investigate the transition from strange nonchaotic to strange chaotic attractors in quasiperiodically driven dynamical systems. It is found that whether the asymptotic attractor of the system is strange nonchaotic or strange chaotic is determined by the relative weight of the contraction and expansion for infinitesimal vectors along a typical trajectory on the attractor. When the average contraction dominates the average expansion, the attractor is strange nonchaotic. Strange chaotic attractors arise when the average expansion dominates the average contraction. The transition from strange nonchaotic to strange chaotic attractors occurs when the average contraction and expansion are balanced. A characteristic signature of this route to chaos is that the Lyapunov exponent passes through zero linearly. We provide numerical confirmation using both a quasiperiodically driven map and a quasiperiodic flow.

AB - We investigate the transition from strange nonchaotic to strange chaotic attractors in quasiperiodically driven dynamical systems. It is found that whether the asymptotic attractor of the system is strange nonchaotic or strange chaotic is determined by the relative weight of the contraction and expansion for infinitesimal vectors along a typical trajectory on the attractor. When the average contraction dominates the average expansion, the attractor is strange nonchaotic. Strange chaotic attractors arise when the average expansion dominates the average contraction. The transition from strange nonchaotic to strange chaotic attractors occurs when the average contraction and expansion are balanced. A characteristic signature of this route to chaos is that the Lyapunov exponent passes through zero linearly. We provide numerical confirmation using both a quasiperiodically driven map and a quasiperiodic flow.

UR - http://www.scopus.com/inward/record.url?scp=0003145080&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0003145080&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0003145080

VL - 53

SP - 57

EP - 65

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 1 SUPPL. A

ER -