On global properties of time-delayed feedback control: Weakly nonlinear analysis

  • Just W
  • Benner H
  • Von Loewenich C
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Abstract

We address the problem which type of initial state yields successful stabilisation when time-delayed feedback control is applied. Using well known concepts from bifurcation theory we provide a general mechanism that limits the corresponding basins of attraction. Application of normal form analysis to general delay-differential equations proves the universality of our results. The empirical criteria which determine the prospective size of the basin are easily accessible and a demonstration in terms of a simple numerical simulation is provided. © 2004 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Codimension two bifurcations
  • Control of chaos
  • Differential-difference equations
  • Hysteresis

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Authors

  • Wolfram Just

  • Hartmut Benner

  • Clemens Von Loewenich

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