Spurious detection of phase synchronization in coupled nonlinear oscillators.

Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with the 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 bandpass 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 bandwidth range, bandpass filtering reduces the effect of noise but can lead to a spurious increase in the degree of phase synchronization with narrowing bandwidth, even when the coupling between the two oscillators remains the same.