We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic fluctuations with a given distribution ψ(τ) of residence...

In this article, the authors discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. The authors find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent...

The brain is probably the most interesting example of a complex network having 1/f variability as determined through the analysis of EEG time series and magnetoencephalogram recordings. Herein we develop a theory of 1/f noise of human cognition to explain the recent experimental observations...