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Shadowing in hidden attractors

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Abstract

Hidden attractors found in physical systems are different from self-exited attractors and may have a small basin of attraction. The issue of shadowing in these attractors using dynamical noise is discussed. We have particularly considered two classes of dynamical systems which have hidden attractors in their state space. In one of the systems, there is no fixed point but only a hidden attractor in the state space, while in the other, the system has one unstable fixed point along with a hidden attractor in the state space. The effect of dynamical noise on these dynamical systems is studied by using the Hausdorff distance between the noisy and deterministic attractors. It appears that, up to some threshold value of noise, the noisy trajectory completely shadows the noiseless trajectory in these attractors which is quite different from the results of self-exited attractors. We compare the results of hidden chaotic attractors with the self-exited chaotic attractors.

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Acknowledgements

Authors acknowledge the support from DST-RFBR for joint Indo–Russian collaborative research project (INT/RUS/RFBR/P-230 and 16-51-45002).

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Authors and Affiliations

  1. Department of Physics, Central University of Rajasthan, Ajmer, Rajasthan, 305817, India

    N. K. Kamal & M. D. Shrimali

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

    V. Varshney & A. Prasad

  3. Department of Applied Cybernetics, Saint Petersburg State University, Saint Petersburg, Russia

    N. V. Kuznetsov & G. A. Leonov

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

    N. V. Kuznetsov

Authors
  1. N. K. Kamal
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  2. V. Varshney
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  3. M. D. Shrimali
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  4. A. Prasad
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  5. N. V. Kuznetsov
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  6. G. A. Leonov
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Correspondence to M. D. Shrimali.

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Kamal, N.K., Varshney, V., Shrimali, M.D. et al. Shadowing in hidden attractors. Nonlinear Dyn 91, 2429–2434 (2018). https://doi.org/10.1007/s11071-017-4022-z

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  • DOI: https://doi.org/10.1007/s11071-017-4022-z

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