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

TL;DR

This paper demonstrates that synchronization in coupled oscillators can induce Taylor's law, with strong synchronization leading to waveform proportionality and a TL exponent of 2, providing insights into the relationship between mean and variance.

Contribution

It reveals that synchronization causes Taylor's law in oscillators and explains the origin of the TL exponent close to 2, combining analytical and numerical methods.

Findings

Synchronization induces Taylor's law in oscillators.

Strong synchronization results in waveform proportionality.

Temporal and spatial TLs have an exponent of 2 under synchronization.

Abstract

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.