Controlling unstable chaos: Stabilizing chimera states by feedback
- Sieber, Jan
- Omel'chenko, Oleh
- Wolfrum, Matthias
2010 Mathematics Subject Classification
- 34H10 34C15
2008 Physics and Astronomy Classification Scheme
- 05.45.Gg, 05.45.Xt, 89.75.Kd
- chaos control, chimera state
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.
- Phys. Rev. Lett., 112 (2014) pp. 054102/1--054102/5.