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Manifestation of strange nonchaotic attractors in extended systems: a study through out-of-time-ordered correlators

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Abstract

We study the spatial spread of out-of-time-ordered correlators (OTOCs) in coupled map lattices (CMLs) of quasiperiodically forced nonlinear maps. We use instantaneous speed (IS) and finite-time Lyapunov exponents (FTLEs) to investigate the role of strange non-chaotic attractors (SNAs) on the spatial spread of the OTOC. We find that these CMLs exhibit a characteristic on and off type of spread of the OTOC for SNA. Further, we provide a broad spectrum of the various dynamical regimes in a two-parameter phase diagram using IS and FTLEs. We substantiate our results by confirming the presence of SNA using established tools and measures, namely the distribution of finite-time Lyapunov exponents, phase sensitivity, spectrum of partial Fourier sums, and 0–1 test.

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Data availibility statement

No external data set is required for this study. The data used in this paper was generated from the equations provided. This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All the data used in this paper can be obtained from the respective equations within the manuscript, and there is no need to provide or deposit the data.]

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Acknowledgements

The work of P.M. is supported by CSIR (Grant No. 03(1422)/18/EMR-II), DST-SERB (Grant No. CRG/2019/004059), DST-FIST under Grant No. SR/FST/PSI-204/2015(C), MHRD RUSA 2.0 (Physical Sciences) and DST-PURSE (Phase-II) Programmes. The work of M.S. forms a part of a research project sponsored by CSIR, India (Grant No. 03(1397)/17/EMR-II). M.S. also acknowledges MHRD RUSA 2.0 (Physical Sciences) and DST-PURSE (Phase-II) Programmes for providing financial support.

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Authors and Affiliations

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

    P. Muruganandam

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

    M. Senthilvelan

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  1. P. Muruganandam
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  2. M. Senthilvelan
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PM and MS contributed equally to this work and writing.

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Correspondence to P. Muruganandam.

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Muruganandam, P., Senthilvelan, M. Manifestation of strange nonchaotic attractors in extended systems: a study through out-of-time-ordered correlators. Eur. Phys. J. B 95, 124 (2022). https://doi.org/10.1140/epjb/s10051-022-00390-1

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