WIAS Preprint No. 1122, (2006)

Control of unstable steady states by strongly delayed feedback


  • Yanchuk, Serhiy
  • Wolfrum, Matthias
    ORCID: 0000-0002-4278-2675
  • Hövel, Philipp
  • Schöll, Eckehard

2008 Physics and Astronomy Classification Scheme

  • 05.45.-a 05.45.Gg 02.30.Ks


  • delayed feedback, large delay, control




We present an asymptotic analysis of time-delayed feedback control of steady states for large delay time. By scaling arguments, and a detailed comparison with exact solutions, we establish the parameter ranges for successful stabilization of an unstable fixed point of focus type. Insight into the control mechanism is gained by analysing the eigenvalue spectrum, which consists of a pseudo-continuous spectrum and up to two strongly unstable eigenvalues. Although the standard control scheme generally fails for large delay, we find that if the uncontrolled system is sufficiently close to its instability threshold, control does work even for relatively large delay times.

Appeared in

  • Phys. Rev. E, 74 (2006) pp. 026201/1--026201/7.

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