L\'evy flights in inhomogeneous environments and 1/f noise

Abstract

Complex dynamical systems which are governed by anomalous diffusion often can be described by Langevin equations driven by L\'evy stable noise. In this article we generalize nonlinear stochastic differential equations driven by Gaussian noise and generating signals with 1/f power spectral density by replacing the Gaussian noise with a more general L\'evy stable noise. The equations with the Gaussian noise arise as a special case when the index of stability alpha=2. We expect that this generalization may be useful for describing 1/f fluctuations in the systems subjected to L\'evy stable noise.