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Chimera states in a class of hidden oscillatory networks

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Abstract

We have identified the chimera states in a class of non-locally coupled network of hidden oscillators without equilibrium, with one and two stable equilibria. All these cases exhibit hidden chaotic oscillations when isolated. We show that the choice of initial conditions is crucial to observe chimeras in these hidden oscillatory networks. The observed states are quantified and delineated with an aid of the incoherence measure. In addition, we computed the basin stability of the obtained chimeras and found that the models without equilibrium and with one equilibrium are diverging to infinity past certain interaction strength. Interestingly, for a no equilibrium model the separation of two incongruous units follows a power law as a function of coupling strength. Remarkably, we detected that the model with one stable equilibrium manifests multi-clustered chimera states owing to its multi-stability.

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Acknowledgements

The authors would like to acknowledge the funding support by DST-RSF project vide grant no. INT/RUS/RSF/P-18 and 19-41-02002. AP extends his gratitude to loE, University of Delhi, for FRP grant.

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Authors and Affiliations

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

    M. Paul Asir & Manish Dev Shrimali

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

    Awadhesh Prasad

  3. Department of Applied cybernetics, Saint Petersburg University, St. Petersburg, Russia

    N. V. Kuznetsov

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

    N. V. Kuznetsov

  5. Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg, Russia

    N. V. Kuznetsov

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  1. M. Paul Asir
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Correspondence to Manish Dev Shrimali.

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Paul Asir, M., Prasad, A., Kuznetsov, N.V. et al. Chimera states in a class of hidden oscillatory networks. Nonlinear Dyn 104, 1645–1655 (2021). https://doi.org/10.1007/s11071-021-06355-w

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  • DOI: https://doi.org/10.1007/s11071-021-06355-w

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