WIAS Preprint No. 1859, (2013)

Controlling unstable chaos: Stabilizing chimera states by feedback



Authors

  • Sieber, Jan
  • Omel'chenko, Oleh
    ORCID: 0000-0003-0526-1878
  • Wolfrum, Matthias

2010 Mathematics Subject Classification

  • 34H10 34C15

2008 Physics and Astronomy Classification Scheme

  • 05.45.Gg, 05.45.Xt, 89.75.Kd

Keywords

  • chaos control, chimera state

Abstract

We present a control scheme that is able to find and stabilize a chaotic saddle in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it loses its attractivity. Similar to a classical delayed feedback control, the scheme is non-invasive, however, only in an appropriately relaxed sense considering the chaotic regime as a statistical equilibrium displaying random fluctuations as a finite size effects. We demonstrate the control scheme for so called chimera states, which are coherence-incoherence patterns in coupled oscillator systems. The control makes chimera states observable close to coherence, for small numbers of oscillators, and for random initial conditions.

Appeared in

  • Phys. Rev. Lett., 112 (2014) pp. 054102/1--054102/5.

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