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Complex mixed-mode oscillations in oscillators sharing nonlinearity

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Abstract

Mixed-mode oscillations (MMOs) are a typical manifestation of slow-fast dynamical systems that contains a sequence of large amplitude excursions interspersed with small amplitude oscillations. We identified complex forms of MMOs in a system of three coupled non-autonomous LCR oscillators sharing a common nonlinearity. Different sequences of MMOs and related dynamics like MMO incrementing bifurcations, Farey sequences, and amplitude-modulated spiking have been witnessed in the model as a consequence of 2-slow and 1-fast external driving frequencies. For particular parametric space, the period adding sequence of MMOs is found to follow a devil’s staircase structure. The transition between states is found to occur via torus canards explosion. We validate our observations through numerical investigation.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The authors confirm that the data supporting the findings of this study are available within the article.]

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Acknowledgements

DP gratefully acknowledges that this work is funded by the Center for Nonlinear Systems, Chennai Institute of Technology (CIT), India, vide funding number CIT/CNS/2021/RP-015. KS thank the DST-SERB, Government of India, for providing National Post Doctoral fellowship under the Grant No. PDF/2019/001589.

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Authors and Affiliations

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

    M. Paul Asir

  2. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamil Nadu, 600 069, India

    D. Premraj & K. Sathiyadevi

  3. Department of Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli, Tamil Nadu, 620024, India

    K. Sathiyadevi

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  1. M. Paul Asir
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  2. D. Premraj
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  3. K. Sathiyadevi
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All the authors contributed equally to the preparation of this manuscript.

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Asir, M.P., Premraj, D. & Sathiyadevi, K. Complex mixed-mode oscillations in oscillators sharing nonlinearity. Eur. Phys. J. Plus 137, 282 (2022). https://doi.org/10.1140/epjp/s13360-022-02498-w

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