  Taylor's law (TL), the scaling relationship between the mean and variance,
has been observed in various fields. However, the underlying reasons why TL is
so widely observed, why the exponents of TL are often 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 exponent 2. Our study can help infer the existence of
synchronization solely from the relationship between the mean and variance.
