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

Author:

Yuzuru Mitsui, Hiroshi Kori

Keyword:

Nonlinear Sciences, Adaptation and Self-Organizing Systems, Adaptation and Self-Organizing Systems (nlin.AO)

journal:

date:

2023-08-03 16:00:00

Abstract

Taylor's law (TL) represents the scaling relationship between the mean and variance derived from population ecology. Recently, it has been observed in various other fields, including biophysics and network dynamics. However, the reasons underlying the frequent appearance of TL, why the exponents of TL are often close to 2, and the relationship between temporal and spatial TLs are not fully understood. Therefore, in this study, using coupled oscillator models, we demonstrated that synchronization can induce TL. In particular, we analytically showed that strong oscillator synchronization leads to waveform proportionality, and thus, temporal and spatial TLs with exponent 2 are derived. Numerical simulations demonstrated excellent agreement with the derived analytical expression. Our study could help to infer the existence of synchronization solely from the relationship between the mean and variance.

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