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Taylor's law (TL), the scaling relationship between the mean and variance,has been observed in various fields. However, the underlying reasons why TL isso widely observed, why the exponents of TL are often close to 2, and therelationship between temporal and spatial TLs are not fully understood. Here,using coupled oscillator models, we analytically and numerically demonstratethat synchronization can induce TL. In particular, we show that strongsynchronization leads to waveform proportionality, resulting in temporal andspatial TLs with exponent 2. Our study can help infer the existence ofsynchronization solely from the relationship between the mean and variance.

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