Recovering detailed shape of phase response curves from the higher harmonics of singularity response

The phase response curve (PRC) is crucial in elucidating the synchronization characteristics of nonlinear oscillators under the influence of external forces. Oscillatory phenomena in nature often consist of an ensemble of multiple oscillators, which complicates the measurement of individual oscillator PRCs. A prior study introduced a technique for estimating individual PRCs from the singularity response (SR)—the reaction of an ensemble of desynchronized oscillators without couplings. However, the utility of this method is somewhat limited, as it considers only the first harmonic of the PRC. The current study demonstrates that the detailed contour of the PRC can be ascertained by employing the higher harmonics of the SR.