Intermingled fractal Arnold tongues

V. Paar and N. Pavin
Phys. Rev. E 57, 1544 – Published 1 February 1998
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Abstract

We present a pattern of multiply interwoven Arnold tongues in the case of the single-well Duffing oscillator at low dissipation and weak forcing: Strips of 22 Arnold tongues form a truncated fractal structure and the tonguelike regions in between are filled by finely intermingled fractal-like 11 and 33 Arnold tongues, which are fat fractals characterized by the uncertainty exponent α0.7. The truncated fractal Arnold tongues are present in the case of high dissipation as well, while the intermingled fractal pattern gradually disappears with increasing dissipation.

  • Received 6 March 1997

DOI:https://doi.org/10.1103/PhysRevE.57.1544

©1998 American Physical Society

Authors & Affiliations

V. Paar and N. Pavin

  • Department of Physics, Faculty of Science, University of Zagreb, Zagreb, Croatia

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Vol. 57, Iss. 2 — February 1998

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