Waveform Proportionality and Taylor’s Law Induced by Synchronization of Periodic and Chaotic Oscillators

Taylor's law (TL), the scaling relationship between mean and variance, has been observed in various fields. However, the underlying reasons for the widespread occurrence of TL, the frequent appearance of the TL exponent value close to 2, and the relationship between temporal and spatial TLs are not fully understood. Here, using coupled oscillator models, we analytically and numerically demonstrate that synchronization can induce TL. In particular, we show that strong synchronization leads to waveform proportionality, resulting in temporal and spatial TLs with an exponent 2. Our results can help infer the existence of synchronization solely from the correlation between mean and variance.