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Multilayered bubbling route to SNA in a quasiperiodically forced electronic circuit with a simple nonlinear element

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Abstract

A new route to strange nonchaotic attractors (SNAs), known as multilayered bubble route to SNA, has been identified in a quasiperiodically forced series \(\textit{LCR}\) circuit with a simple nonlinear element. Upon increasing the control parameter, the stable orbits of the torus become unstable, which induces formation of bubbles in the neighbourhood of the resonating region of the torus. We have observed three tori with three smooth branches in the Poincaré map which gradually loose their smoothness and ultimately approach bubble formation, and then approach fractal behaviour via SNAs before the onset of chaos. The bubbles gradually enlarge and subsequently another three layers of bubbles are formed as a function of the control parameter. The layers get increasingly wrinkled as a function of the control parameter, resulting in the creation of SNAs which are charaterized by Poincaré maps. Apart from the multilayered bubble route to SNA, Heagy–Hammel and fractalization routes to SNA have also been numerically observed and are characterized qualitatively interms of phase portraits, power spectrum. The above mentioned three routes are further characterized quantitatively, by singular-continuous spectrum analysis, phase sensitivity measure, distribution of finite time Lyapunov exponents, largest Lyapunov exponent and its variance.

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Authors and Affiliations

  1. Department of Physics, St. John’s College, Palayamkottai, 627 002, India

    A. Arulgnanam

  2. Department of Physics and Astrophysics, University of Delhi, Delhi, 110 007, India

    Awadesh Prasad

  3. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli, 620 024, India

    K. Thamilmaran & M. Daniel

Authors
  1. A. Arulgnanam
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  2. Awadesh Prasad
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  3. K. Thamilmaran
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  4. M. Daniel
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Correspondence to K. Thamilmaran.

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Arulgnanam, A., Prasad, A., Thamilmaran, K. et al. Multilayered bubbling route to SNA in a quasiperiodically forced electronic circuit with a simple nonlinear element. Int. J. Dynam. Control 4, 413–427 (2016). https://doi.org/10.1007/s40435-015-0154-5

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  • DOI: https://doi.org/10.1007/s40435-015-0154-5

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