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Author: Omel'chenko, Oleh × Subject: partial synchronization ×

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    Spectral properties of chimera states
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Wolfrum, Matthias; Omel'chenko, Oleh; Yanchuk, Serhiy; Maistrenkko, Yuri
    Literaturverz. Chimera states are particular trajectories in systems of phase oscillators with nonlocal coupling that display a pattern of coherent and incoherent motion. We present here a detailed analysis of the spectral properties for such trajectories. First, we study numerically their Lyapunov spectrum and its behavior for an increasing number of oscillators. The spectra demonstrate the hyperchaotic nature of the chimera states and show a correspondence of the Lyapunov dimension with the number of incoherent oscillators. Then, we pass to the thermodynamic limit equation and present an analytic approach to the spectrum of a corresponding linearized evolution operator. We show that in this setting, the chimera state is neutrally stable and that the continuous spectrum coincides with the limit of the hyperchaotic Lyapunov spectrum obtained for the finite size systems.
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    Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally coupled phase oscillators
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Omel'chenko, Oleh; Wolfrum, Matthias; Yanchuk, Serhiy; Maistrenko, Yuri; Sudakov, Oleksandr
    Recently it has been shown that large arrays of identical oscillators with non-local coupling can have a remarkable type of solutions that display a stationary macroscopic pattern of coexisting regions with coherent and incoherent motion, often called chimera states. We present here a detailed numerical study of the appearance of such solutions in twodimensional arrays of coupled phase oscillators. We discover a variety of stationary patterns, including circular spots, stripe patterns, and patterns of multiple spirals. Here, the stationarity means that for increasing system size the locally averaged phase distributions tend to the stationary profile given by the corresponding thermodynamic limit equation