title: Controlling unstable chaos: stabilizing chimera states by feedback.
abstract: We present a control scheme that is able to find and stabilize an unstable chaotic regime 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 classical delayed feedback control, the scheme is noninvasive, however only in an appropriately relaxed sense considering the chaotic regime as a statistical equilibrium displaying random fluctuations as a finite size effect. 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.
authors.affiliation: College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF, United Kingdom.
authors.forename: Jan
authors.initials: J
authors.lastname: Sieber
authors.affiliation: Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany and Institute of Mathematics, National Academy of Sciences of Ukraine, Tereschenkivska Street 3, 01601 Kyiv, Ukraine.
authors.forename: Oleh E
authors.initials: OE
authors.lastname: Omel'chenko
authors.affiliation: Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Wolfrum