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Spectral element method and the delayed feedback control of chaos

Publication ,  Journal Article
Tweten, DJ; Mann, BP
Published in: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
October 31, 2012

A spectral element approach is introduced to determine the Floquet exponents (FEs) of unstable periodic orbits (UPOs) stabilized by extended delayed feedback control (EDFC). The spectral approach does not require solving time-dependent eigenproblems that existing methods require. Instead, the spectral approach determines the stability of the delay differential equations of the system by numerical approximation. The method is capable of analyzing systems whose UPOs arise from bifurcations other than period-doubling. Results are presented for stabilizing UPOs in Duffing systems. The FEs calculated by the spectral approach are compared to published results for two examples. In both cases, the spectral method results agree well with those determined by previous methods. In addition, the spectral method was used to analyze a high-dimensional, asymmetrical system with a UPO in chaos arising from tori doubling following a Hopf bifurcation. © 2012 American Physical Society.

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Published In

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

October 31, 2012

Volume

86

Issue

4

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Tweten, D. J., & Mann, B. P. (2012). Spectral element method and the delayed feedback control of chaos. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 86(4). https://doi.org/10.1103/PhysRevE.86.046214
Tweten, D. J., and B. P. Mann. “Spectral element method and the delayed feedback control of chaos.” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 86, no. 4 (October 31, 2012). https://doi.org/10.1103/PhysRevE.86.046214.
Tweten DJ, Mann BP. Spectral element method and the delayed feedback control of chaos. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2012 Oct 31;86(4).
Tweten, D. J., and B. P. Mann. “Spectral element method and the delayed feedback control of chaos.” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 86, no. 4, Oct. 2012. Scopus, doi:10.1103/PhysRevE.86.046214.
Tweten DJ, Mann BP. Spectral element method and the delayed feedback control of chaos. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2012 Oct 31;86(4).

Published In

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

October 31, 2012

Volume

86

Issue

4

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences