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The AC Driven Frenkel-Kontorova Model: From Shapiro Steps to Chaos

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13th Chaotic Modeling and Simulation International Conference (CHAOS 2020)

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Abstract

The appearance of devil’s staircase and chaos have been studied in the dc+ac driven Frenkel-Kontorova model. In the overdamped limit, the devil’s staircase structure arising from the complete mode-locking of an entirely nonchaotic system was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. When the inertial term is included, unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase.

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Acknowledgement

This work was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Grant no. 451-03-9/2021-14/200017 (University of Belgrade, Institute of Nuclear Sciences “Vinča”) and by the Provincial Secretariat for High Education and Scientific Research of Vojvodina (Project No. APV 114-451-2201). The work was funded by the project 18-71-10095 of the Russian National Fund.

Author information

Authors and Affiliations

  1. Laboratory for Theoretical and Condensed Matter Physics - 020, “Vinča” Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, 522, 11001, Belgrade, Serbia

    Jasmina Tekić

  2. Department of Physics, University of South Africa, Science Campus, Private Bag X6, Florida Park, 1710, South Africa

    Andre Botha

  3. Department of Physics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Petar Mali

  4. BLTP, JINR, Dubna, Moscow Region, 141980, Russia

    Yuri M. Shukrinov

  5. Dubna State University, Dubna, 141980, Russia

    Yuri M. Shukrinov

Authors
  1. Jasmina Tekić
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  2. Andre Botha
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  3. Petar Mali
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  4. Yuri M. Shukrinov
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Corresponding author

Correspondence to Jasmina Tekić .

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Editors and Affiliations

  1. ManLab, Technical University of Crete, Chania, Greece

    Christos H. Skiadas

  2. Department of Management Science and Technology, Hellenic Mediterranean University, Agios Nikolaos, Crete, Lasithi, Greece

    Yiannis Dimotikalis

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Tekić, J., Botha, A., Mali, P., Shukrinov, Y.M. (2021). The AC Driven Frenkel-Kontorova Model: From Shapiro Steps to Chaos. In: Skiadas, C.H., Dimotikalis, Y. (eds) 13th Chaotic Modeling and Simulation International Conference. CHAOS 2020. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-70795-8_65

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