On the 1/f fluctuations in the nonlinear systems affected by noise

TL;DR

This paper explores the conditions under which 1/f fluctuations emerge in simple nonlinear systems influenced by external noise, identifying when and how these fluctuations occur across different parameters.

Contribution

It provides a detailed analysis of the necessary and sufficient conditions for 1/f fluctuations in noisy nonlinear systems, highlighting their dependence on system parameters.

Findings

1/f fluctuations occur only within specific frequency ranges.

The presence of external noise can induce 1/f behavior under certain conditions.

The behavior depends on system parameters and external perturbations.

Abstract

We investigate a problem of the necessary and sufficient conditions for appearance of the 1/f fluctuations in the simple systems affected by the external random perturbations, i.e. the power spectral density of the flux of particles moving in some contours and perturbed by the external forces. In some cases we observe the 1/f behavior but only in some range of frequencies and parameters of the systems.