WIAS Preprint No. 1577, (2010)

Spectral properties of chimera states


  • Wolfrum, Matthias
    ORCID: 0000-0002-4278-2675
  • Omel'chenko, Oleh
    ORCID: 0000-0003-0526-1878
  • Yanchuk, Serhiy
  • Maistrenko, Yuri

2010 Mathematics Subject Classification

  • 37M25 37N20 37N25

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt, 89.75.Kd


  • coupled phase oscillators, partial synchronization, Lyapunov spectrum




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.

Appeared in

  • Chaos, 21 (2011) pp. 013112 (8 pages).

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