耦合非线性振子相位同步的寄生检测
Spurious detection of phase synchronization in coupled nonlinear oscillators
摘要：
耦合非线性系统在一定的条件下表现出相位同步，这可能会改变不同的频带或存在的附加系统噪声。在这两种情况下，傅立叶滤波传统上用于预处理数据。我们研究了两个耦合罗斯勒振荡器的相位同步在多大程度上取决于（1）它们的功率谱的宽度，（2）带通滤波器的宽度，和（3）附加噪声的水平。我们发现，对于相同的耦合强度，振荡器具有较宽的功率谱表现出较弱的同步。此外，我们发现，在一个宽的带宽范围内，带通滤波降低了噪声的影响，但可以导致一个虚假的增加，即使当两个振荡器之间的耦合保持不变的同步程度与窄带宽。
英文摘要：
Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess data. We investigate to what extent the phase synchronization of two coupled Rössler oscillators depends on (1) the broadness of their power spectrum, (2) the width of the band-pass filter, and (3) the level of added noise. We find that for identical coupling strengths, oscillators with broader power spectra exhibit weaker synchronization. Further, we find that within a broad band width range, band-pass filtering reduces the effect of noise but can lead to a spurious increase in the degree of synchronization with narrowing band width, even when the coupling between the two oscillators remains the same.
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