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High-order synchronization in a system of nonlinearly coupled Stuart-Landau oscillators

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Abstract

The high-order synchronization was studied in systems driven by external force and in autonomous systems with proper frequency mismatch. Differing from the literature, in this article, we demonstrate the occurrence of high-order (1 : 2) synchronization in an autonomous nonlinearly coupled (Stuart-Landau) oscillators which admit a particular form of rotational symmetry. Interestingly, the observed 1 : 2 synchronization happens not only for a particular choice of natural frequencies but for all possible choices of frequencies. We have observed such a behaviour in the case of 1 : 1 synchronization, where we have seen a variety of couplings in the literature that forces the oscillators to have almost equal frequencies and makes the system to oscillate with a common frequency independent of whether the oscillators are identical or non-identical. Similarly, in this article we observe that, whether the initial choice of frequencies is of the ratio 1 : 2 or not, the given nonlinear coupling forces the system to oscillate with the frequency ratio 1 : 2. Further, we present synchronization and other dynamical behaviours of the system by considereing different choices of natural frequencies.

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Data Availibility Statement

This manuscript has associated data in a data repository [Authors’ comment: All data generated or analysed during this study are included in this published article [https://doi.org/10.1140/epjp/s13360-021-02216-y] and its supplementary information files.]

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Acknowledgements

NT wishes to thank National Board for Higher Mathematics, Government of India, for providing the Junior Research Fellowship under the Grant No. 02011/20/2018 NBHM (R.P)/R&D II/15064. The work of MS forms part of a research project sponsored by Council of Scientific and Industrial Research, Government of India, under the Grant No. 03/1397/17/EMR-II.

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Authors and Affiliations

  1. Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli, Tamil Nadu, 620024, India

    Nissi Thomas, S. Karthiga & M. Senthilvelan

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  1. Nissi Thomas
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  2. S. Karthiga
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  3. M. Senthilvelan
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All the authors contributed equally to the preparation of this manuscript.

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Correspondence to M. Senthilvelan .

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Thomas, N., Karthiga, S. & Senthilvelan , M. High-order synchronization in a system of nonlinearly coupled Stuart-Landau oscillators. Eur. Phys. J. Plus 136, 1222 (2021). https://doi.org/10.1140/epjp/s13360-021-02216-y

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