# American Institute of Mathematical Sciences

January  2016, 36(1): 451-467. doi: 10.3934/dcds.2016.36.451

## Eliminating restrictions of time-delayed feedback control using equivariance

 1 Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany, Germany

Received  June 2014 Revised  May 2015 Published  June 2015

Pyragas control is a widely used time-delayed feedback control for the stabilization of periodic orbits in dynamical systems. In this paper we investigate how we can use equivariance to eliminate restrictions of Pyragas control, both to select periodic orbits for stabilization by their spatio-temporal pattern and to render Pyragas control possible at all for those orbits. Another important aspect is the optimization of equivariant Pyragas control, i.e. to construct larger control regions. The ring of $n$ identical Stuart-Landau oscillators coupled diffusively in a bidirectional ring serves as our model.
Citation: Isabelle Schneider, Matthias Bosewitz. Eliminating restrictions of time-delayed feedback control using equivariance. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 451-467. doi: 10.3934/dcds.2016.36.451
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