Intermittency route to strange nonchaotic attractors in a non-skew-product map

Takahito Mitsui, Yoji Aizawa

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Whether strange nonchaotic attractors (SNAs) can typically arise in non-skew-product maps has been a crucial question for more than two decades. Recently, it was shown that SNAs arise in a particular non-skew-product map related to quasiperiodically driven continuous dynamical systems. In the present paper, we derive Badard's non-skew-product map from a periodically driven continuous dynamical system with spatially quasiperiodic potential and investigate onset mechanisms of SNAs in the map. In particular, we focus on a transition route to intermittent SNAs, where SNAs appear after pair annihilations of stable and unstable fixed points located on a ring-shaped invariant curve. Then the mean residence time and rotation numbers have a logarithmic singularity. Finally, we discuss the existence of SNAs in a special class of non-skew-product maps.

Original languageEnglish
Article number046210
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume81
Issue number4
DOIs
Publication statusPublished - 2010 Apr 21

Fingerprint

strange attractors
Strange attractor
Intermittency
intermittency
routes
products
dynamical systems
Dynamical system
Invariant Curves
Residence Time
Rotation number
Annihilation
Logarithmic
Unstable
Fixed point
Singularity
Ring
rings
curves

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Intermittency route to strange nonchaotic attractors in a non-skew-product map. / Mitsui, Takahito; Aizawa, Yoji.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 81, No. 4, 046210, 21.04.2010.

Research output: Contribution to journalArticle

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