Bifurcation to strange nonchaotic attractors

Tolga Yaiçinkaya, Ying-Cheng Lai

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

Strange nonchaotic attractors are attractors that are geometrically strange, but have nonpositive Lyapunov exponents. These attractors occur in regimes of nonzero Lebesgue measure in the parameter space of quasiperiodically driven dissipative dynamical systems. We investigate a route to strange nonchaotic attractors in systems with a symmetric invariant subspace. Assuming there is a quasiperiodic torus in the invariant subspace, we show that the loss of the transverse stability of the torus can lead to the birth of a strange nonchaotic attractor. A physical phenomenon accompanying this route to strange nonchaotic attractors is an extreme type of intermittency. We expect this route to be physically observable, and we present theoretical arguments and numerical examples with both quasiperiodically driven maps and quasiperiodically driven flows. The transition to chaos from the strange nonchaotic behavior is also studied.

Original languageEnglish (US)
Pages (from-to)1623-1630
Number of pages8
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume56
Issue number2
StatePublished - Aug 1997
Externally publishedYes

Fingerprint

strange attractors
Strange attractor
Bifurcation
routes
Invariant Subspace
Attractor
Torus
Dissipative Dynamical System
Intermittency
intermittency
Lebesgue Measure
Lyapunov Exponent
dynamical systems
Parameter Space
chaos
Chaos
Extremes
Transverse
exponents
Numerical Examples

ASJC Scopus subject areas

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

Cite this

Bifurcation to strange nonchaotic attractors. / Yaiçinkaya, Tolga; Lai, Ying-Cheng.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 56, No. 2, 08.1997, p. 1623-1630.

Research output: Contribution to journalArticle

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