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Stochastic nonlinear differential equation generating 1/f noise.

B Kaulakys¹, J Ruseckas

¹Institute of Theoretical Physics and Astronomy, Vilnius University, A. Gostauto 12, LT-01108 Vilnius, Lithuania. kaulakys@itpa.lt

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 28, 2004

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We derived a nonlinear stochastic differential equation that generates 1/f noise across a wide frequency range. Numerical solutions confirm this equation produces power-law distributions, demonstrating a new model for 1/f noise processes.

Area of Science:

Physics
Nonlinear Dynamics
Stochastic Processes

Background:

1/f noise, also known as pink noise, is prevalent in various natural and artificial systems.
Previous models often lack a unified framework applicable across wide frequency ranges.
Understanding the underlying stochastic processes is crucial for signal analysis.

Purpose of the Study:

To derive a stochastic nonlinear differential equation that generates 1/f noise.
To demonstrate that the derived equation produces power-law distributions.
To provide a theoretical and numerical framework for 1/f noise processes.

Main Methods:

Development of a stochastic nonlinear differential equation from a point process model.
Derivation of the general Langevin equation with multiplicative noise.

Related Experiment Videos

Numerical solutions of the derived equation with restricted diffusion.

Main Results:

A novel stochastic differential equation capable of generating 1/f noise is derived.
The solutions to this equation exhibit characteristic power-law distributions.
Numerical simulations validate the theoretical model across a defined frequency spectrum.

Conclusions:

The derived stochastic differential equation offers a robust model for 1/f noise.
This model successfully reproduces the power-law behavior associated with 1/f noise.
The findings provide a new tool for analyzing and simulating systems exhibiting 1/f noise.