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Time varying feedback control on multi-stability in hidden attractor

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Abstract

We study a on-off feedback method to control the dynamics of a radio physical oscillator having hidden coexisting attractors. The proposed time-varying on-off feedback effectively controls the multi-stability which acts in an on-off manner. We show that for suitable values of feedback strength, feedback active time ratio and time period, the coexisting chaotic and periodic dynamics of the system go to a mono-stable periodic state followed by a stable steady state. This transition from multiple attractors to a single attractor is confirmed by calculating bifurcation diagram, Lyapunov exponent and the basin size as a measure. We also illustrate the generation of chaotic attractor in the system using this scheme.

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Authors and Affiliations

  1. Department of Physics, Central University of Rajasthan, Ajmer, 305 817, India

    Amit Sharma, Kiran Yadav & Manish Dev Shrimali

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

    Awdhesh Prasad

  3. Saint-Petersburg State University, St. Petersburg, Russia

    Nikolay V. Kuznetsov

  4. Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Nikolay V. Kuznetsov

Authors
  1. Amit Sharma
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  2. Kiran Yadav
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  3. Manish Dev Shrimali
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  4. Awdhesh Prasad
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  5. Nikolay V. Kuznetsov
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Correspondence to Manish Dev Shrimali.

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Sharma, A., Yadav, K., Shrimali, M.D. et al. Time varying feedback control on multi-stability in hidden attractor. Eur. Phys. J. Spec. Top. 229, 1245–1255 (2020). https://doi.org/10.1140/epjst/e2020-900167-1

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