Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany.
Chaos. 2011 Mar;21(1):013112. doi: 10.1063/1.3563579.
Chimera states are particular trajectories in systems of phase oscillators with nonlocal coupling that display a spatiotemporal 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.
嵌合体状态是具有非局部耦合的相振荡器系统中的特殊轨迹，表现出相干和非相干运动的时空模式。我们在这里对这些轨迹的谱性质进行了详细的分析。首先，我们通过数值方法研究了它们的 Lyapunov 谱及其随振荡器数量增加的行为。这些谱显示了嵌合体状态的超混沌性质，并表明 Lyapunov 维数与非相干振荡器的数量相对应。然后，我们通过热力学极限方程并提出了相应线性化演化算子谱的解析方法。我们表明，在这种情况下，嵌合体状态是中性稳定的，连续谱与有限大小系统中获得的超混沌 Lyapunov 谱的极限相重合。
