Global warming, extreme climate events, earthquakes and their accompanying
socioeconomic disasters pose significant risks to humanity. Yet due to the nonlinear …

Complex bodily rhythms are ubiquitous in living organisms. These rhythms arise from
stochastic, nonlinear biological mechanisms interacting with a fluctuating environment …

The healthy heartbeat is traditionally thought to be regulated according to the classical
principle of homeostasis whereby physiologic systems operate to reduce variability and …

According to classical concepts of physiologic control, healthy systems are self-regulated to
reduce variability and maintain physiologic constancy. Contrary to the predictions of …

LéVY flights are a special class of random walks whose step lengths are not constant but
rather are chosen from a probability distribution with a power-law tail. Realizations of Lévy …

Fast, accurate algorithm for numerical simulation of Levy stable stochastic processes Page 1
PHYSICAL REVIEW Evolume 49, NUMBER 5 MAY 1994 Fast, accurate algorithm for …

We examine the detrended fluctuation analysis (DFA), which is a well-established method
for the detection of long-range correlations in time series. We show that deviations from …

THE large-scale dynamical properties of some physical systems depend on the dynamical
evolution of a large number of nonlinearly coupled subsystems. Examples include systems …

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-
range power-law correlation exponents in noisy signals. Many noisy signals in real systems …

This text describes the statistcal behavior of complex systems and shows how the fractional
calculus can be used to model the behavior. The discussion emphasizes physical …