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Simple model for 1/f(alpha) noise.

Jörn Davidsen1, Heinz Georg Schuster

  • 1Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität, Olshausenstrasse 40, 24118 Kiel, Germany. jdavidse@chem.utoronto.ca

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
Summary

We developed a simple model generating pulse trains with power-law interval distributions and 1/f noise. This mechanism, using a fluctuating threshold, explains variability in neural activity and seismic data.

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Area of Science:

  • Physics
  • Neuroscience
  • Geophysics

Background:

  • Neural activity and seismic data often exhibit complex temporal patterns, including 1/f noise.
  • Understanding the underlying mechanisms of these phenomena is crucial for various scientific fields.

Purpose of the Study:

  • To introduce a simple stochastic mechanism capable of generating pulse trains with specific statistical properties.
  • To explain the observed 1/f(alpha) power spectrum and power-law distribution of pulse intervals in biological and geophysical systems.

Main Methods:

  • A stochastic model incorporating a fluctuating threshold undergoing Brownian motion.
  • Analysis of pulse interval distributions and power spectra generated by the model.
  • Approximation of pulse intervals using a random walk with multiplicative noise for linearly increasing potentials.

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Main Results:

  • The model successfully generates pulse trains with power-law distributed intervals and a 1/f(alpha) power spectrum (alpha ≈ 1) over several decades.
  • The fluctuating threshold performing Brownian motion is identified as the key component.
  • The model's output aligns with experimental observations in neurobiology and earthquake data.

Conclusions:

  • The proposed stochastic mechanism provides a parsimonious explanation for 1/f noise and high interpulse interval variability.
  • This model bridges findings in neurobiology (cortical neurons) and geophysics (earthquake data).
  • The fluctuating threshold model offers a unified framework for understanding complex temporal dynamics in diverse systems.