History-dependent control of unstable periodic orbits

P. M. Alsing, A. Gavrielides, V. Kovanis

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We present a method of stabilizing unstable periodic orbits in systems whose natural time scales are on the order of or faster than the time it would take for the experimental implementation of the Ott-Grebogi-Yorke (OGY) controlling method [Phys. Rev. Lett. 64, 1196 (1990)]. We determine the controlling perturbation one or more cycles ahead of when it needs to be applied, thereby gaining the additional time necessary to measure a signal, determine the perturbation, and then implement it. Formulas for this method of prior iterate control are derived and their utility is demonstrated numerically on the Hénon map for controlling the unstable orbits of period one and two. The effects of noise on this control method are examined and the results are compared with a similar application of the OGY scheme in the presence of noise.

Original languageEnglish
Pages (from-to)1968-1977
Number of pages10
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume50
Issue number3
DOIs
Publication statusPublished - 1994
Externally publishedYes

Fingerprint

Periodic Orbits
Unstable
histories
orbits
Dependent
perturbation
Perturbation
Iterate
cycles
Time Scales
Orbit
Cycle
Necessary
History

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

History-dependent control of unstable periodic orbits. / Alsing, P. M.; Gavrielides, A.; Kovanis, V.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 50, No. 3, 1994, p. 1968-1977.

Research output: Contribution to journalArticle

Alsing, P. M. ; Gavrielides, A. ; Kovanis, V. / History-dependent control of unstable periodic orbits. In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 1994 ; Vol. 50, No. 3. pp. 1968-1977.
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