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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.10049 |
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| _version_ | 1866915447269490688 |
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| author | Nakamichi, Akika Uesaka, Izumi Morikawa, Masahiro |
| author_facet | Nakamichi, Akika Uesaka, Izumi Morikawa, Masahiro |
| contents | 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 |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamic Synchronization and Resonance as a Universal Origin of 1/f Fluctuations -- Amplitude Modulation Across Music and Nature Nakamichi, Akika Uesaka, Izumi Morikawa, Masahiro Sound Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability 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 |
| title | Dynamic Synchronization and Resonance as a Universal Origin of 1/f Fluctuations -- Amplitude Modulation Across Music and Nature |
| topic | Sound Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2508.10049 |