Detecting synchronization of self-sustained oscillators by external driving with varying frequency.

We propose a method for detecting the presence of a synchronization of a self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of the self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to a driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.