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

Takahito Mitsui, Yoji Aizawa

Research output: Contribution to journalArticlepeer-review

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

ASJC Scopus subject areas

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

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