1/f Noise from nonlinear stochastic differential equations.
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.
Ruseckas
J
J
Institute of Theoretical Physics and Astronomy, Vilnius University, A Gostauto 12, LT-01108 Vilnius, Lithuania. julius.ruseckas@tfai.vu.lt
Kaulakys
B
B
D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D013269:Stochastic Processes