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Spectral properties of chimera states

Please always quote using this URN:urn:nbn:de:0296-matheon-8240
  • Chimera states are particular trajectories in systems of phase oscillators with non-local coupling that display a spatio-temporal 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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Metadaten
Author:Matthias Wolfrum, Oleh Omelchenko, Serhiy Yanchuk, Yuri Maistrenko
URN:urn:nbn:de:0296-matheon-8240
Referee:Alexander Mielke
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/04/29
Release Date:2011/04/29
Tag:
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C15 Nonlinear oscillations, coupled oscillators
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Kxx Functional-differential and differential-difference equations [See also 37-XX] / 34K08 Spectral theory of functional-differential operators
Preprint Number:788
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