Exactly solvable model of continuous stationary 1/f noise

Area of Science:

• Physics
• Dynamical Systems
• Statistical Mechanics

Background:

• 1/f noise, also known as pink noise, is prevalent in various natural and artificial systems.
• Understanding the generation mechanisms of 1/f noise is crucial for analyzing complex phenomena.
• Previous models often lack exact solvability or fail to capture the non-Gaussian characteristics.

Purpose of the Study:

• To present an exactly solvable model for generating continuous random processes exhibiting a 1/f power spectrum.
• To derive an exact formula for the correlation function of 1/f noise.
• To investigate the non-Gaussian properties of the generated 1/f noise.

Main Methods:

• Development of an exactly solvable mathematical model.
• Perturbation of two-dimensional dynamical systems with colored Gaussian noise.
• Derivation of an exact formula for the noise correlation function.
• Calculation of the one-time probability distribution function.

Main Results:

• An exactly solvable model for continuous random processes with a 1/f power spectrum was successfully developed.
• An exact formula relating 1/f noise correlations to the correlations of perturbing colored noises was derived.
• The 1/f spectrum was shown to occur in a diverse range of systems.
• The generated 1/f noise was demonstrated to be non-Gaussian.

Conclusions:

• The presented model provides a robust framework for studying 1/f noise.
• The derived formula offers a powerful tool for analyzing the origins of 1/f noise in different contexts.
• The non-Gaussian nature of the 1/f noise highlights the complexity of the underlying processes.