Controlling unstable chaos: Stabilizing chimera states by feedback

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Date
2013
Journal Title
Journal ISSN
Volume Title
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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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 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 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.

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Keywords
Chaos control, chimera states
Citation
Citation
Sieber, J., Omel’chenko, O., & Wolfrum, M. (2013). Controlling unstable chaos: Stabilizing chimera states by feedback (Version publishedVersion, Vol. 1859). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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