1/f Noise from nonlinear stochastic differential equations

Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Mar;81(3 Pt 1):031105. doi: 10.1103/PhysRevE.81.031105. Epub 2010 Mar 8.


We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fbeta noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fbeta noise, and provides further insights into the origin of 1/fbeta noise.

MeSH terms

  • Algorithms*
  • Computer Simulation
  • Data Interpretation, Statistical*
  • Models, Statistical*
  • Nonlinear Dynamics*
  • Stochastic Processes*