Time-Delay Feedback Control of an Oscillatory Medium

  • Michael StichEmail author
  • Carsten Beta
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 20)


The supercritical Hopf bifurcation is one of the simplest ways in which a stationary state of a nonlinear system can undergo a transition to stable self-sustained oscillations. At the bifurcation point, a small-amplitude limit cycle is born, which already at onset displays a finite frequency. If we consider a reaction-diffusion system that undergoes a supercritical Hopf bifurcation, its dynamics is described by the complex Ginzburg-Landau equation (CGLE). Here, we study such a system in the parameter regime where the CGLE shows spatio-temporal chaos. We review a type of time-delay feedback methods which is suitable to suppress chaos and replace it by other spatio-temporal solutions such as uniform oscillations, plane waves, standing waves, and the stationary state.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Non-linearity and Complexity Research Group, System Analytics Research Institute, School of Engineering and Applied ScienceAston UniversityBirminghamUK
  2. 2.Institute of Physics and AstronomyUniversity of PotsdamPotsdamGermany

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