Temporal and spatial Taylor's law induced by synchronization of periodic and chaotic oscillators

Taylor's law, a scaling relationship between the mean and variance, has been confirmed in various fields. However, the following three questions are unclear. 1. Why is it widely observed especially in ecosystems? 2. Why are the exponents around 2 often recorded in ecosystems? 3. Are the mechanisms of temporal and spatial Taylor's law the same? Here, we show that synchronization, a widely observed phenomenon in ecosystems as well as Taylor's law, can induce Taylor's law. In particular, we find numerically and analytically that strong synchronization, in which time series are proportional to each other, induces temporal and spatial Taylor's law with exponent 2.