Dynamic Synchronization and Resonance as a Universal Origin of 1/f Fluctuations -- Amplitude Modulation Across Music and Nature

TL;DR

This paper introduces a universal physical mechanism based on amplitude modulation and demodulation, explaining the widespread occurrence of 1/f fluctuations across systems like music, seismic activity, and astrophysics, without requiring critical synchronization conditions.

Contribution

It presents a novel framework linking amplitude modulation and demodulation to 1/f fluctuations, supported by models and cross-domain empirical analyses, expanding understanding of natural and engineered system behaviors.

Findings

1/f spectra emerge robustly from AM/DM mechanisms in simulations.

Synchronization and resonance independently produce 1/f fluctuations.

Cross-domain data analyses confirm the universality of the proposed framework.

Abstract

We propose a universal physical mechanism for the emergence of 1/f fluctuations, observed across a wide range of systems. In particular, we verify this on acoustic cases. The mechanism is based on amplitude modulation (AM) and demodulation (DM), where the 1/f spectral law arises not in the raw waveform but in its demodulated amplitude envelope. Two distinct yet complementary processes generate the required AM: (i) stochastic synchronization among oscillators, modeled via an extended Kuramoto framework that captures perpetual synchronization-desynchronization cycles, and (ii) frequency-selective resonance, modeled by spectral accumulation of eigenmodes in acoustic or structural environments. Numerical simulations demonstrate that both mechanisms, acting separately or in combination, robustly produce 1/f spectra over several decades when DM is applied, and that the classical Kuramoto critical point is not necessary for their emergence. We demonstrate the cross-domain relevance of this AM/DM framework through analyses of musical performances, seismic records, and astrophysical time series, revealing a common underlying structure. This work establishes demodulation as a general route to 1/f fluctuations, providing a simple and scalable explanation for its ubiquity in both natural and engineered systems. Keywords: 1/f fluctuation, amplitude modulation, synchronization, resonance, Kuramoto model, music, natural noise, demodulation