Controlling unstable chaos: stabilizing chimera states by feedback

J Sieber, OE Omel'chenko, M Wolfrum - Physical review letters, 2014 - APS
Physical review letters, 2014APS
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 …
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.
American Physical Society
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