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Dynamics of a Large Ring of Unidirectionally Coupled Duffing Oscillators

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IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design

Part of the book series: IUTAM Bookseries (closed) ((IUTAMBOOK,volume 32))

Abstract

In this paper we study the dynamics of a large ring of unidirectionally coupled autonomous Duffing oscillators. We paid our attention to the role of unstable periodic solutions for the appearance of spatio-temporal structures and the Eckhaus effect. We provide an explanation for the fast transition to chaos showing that the parameter interval, where the transition from a stable periodic state to chaos occurs, scales like the inverse square of the number of oscillators in the ring.

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Acknowledgements

The authors acknowledge the support of DFG Research Center Matheon “Mathematics for key technologies” under the projects D8 (M.W.) and D21 (S.Y.). P.P. acknowledges the support from Foundation for Polish Science (the START fellowship).

Author information

Authors and Affiliations

  1. Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924, Lodz, Poland

    P. Perlikowski, A. Stefanski & Tomasz Kapitaniak

  2. Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, 10099, Berlin, Germany

    S. Yanchuk

  3. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany

    M. Wolfrum

Authors
  1. P. Perlikowski
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  2. S. Yanchuk
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  3. M. Wolfrum
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  4. A. Stefanski
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  5. Tomasz Kapitaniak
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Corresponding author

Correspondence to Tomasz Kapitaniak .

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Editors and Affiliations

  1. College of Physical Sciences, Department of Engineering, Centre for, University of Aberdeen, Aberdeen, AB24 3UE, United Kingdom

    Marian Wiercigroch

  2. Structural and Geotechnical Engineering, Sapienza University of Rome, Via A. Gramsci 53, Roma, 00197, Italy

    Giuseppe Rega

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Perlikowski, P., Yanchuk, S., Wolfrum, M., Stefanski, A., Kapitaniak, T. (2013). Dynamics of a Large Ring of Unidirectionally Coupled Duffing Oscillators. In: Wiercigroch, M., Rega, G. (eds) IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design. IUTAM Bookseries (closed), vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5742-4_5

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  • DOI: https://doi.org/10.1007/978-94-007-5742-4_5

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5741-7

  • Online ISBN: 978-94-007-5742-4

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