Bifurcation to strange nonchaotic attractors

Tolga Yalcinkaya, Ying-Cheng Lai

Research output: Contribution to journalArticle

39 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 tonus 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
Pages (from-to)1623-1630
Number of pages8
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume56
Issue number2
DOIs
Publication statusPublished - Aug 1997

Keywords

  • on-off intermittency
  • chaotic attractors
  • riddled basins
  • structure intermediate
  • dynamical-systems
  • transition
  • oscillators
  • spectra
  • birth
  • map

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