We propose a dynamical model generating the same non-Poisson renewal events as those currently found in complex systems as the blinking quantum dots and the human brain. Our results suggest that these complex systems can be interpreted as a set of synchronized neurons.

The combined use of the ‘reduced’ model theory, adiabatic elimination of the fast variables and continued fraction procedure is shown to make it possible to study chemical relaxation in the presence of radiative excitation. This requires that the reaction coordinate be assumed to be slow...

We study the effects of an external periodic perturbation on a Poisson rate process, with special attention to the perturbation-induced sojourn-time patterns. We show that these patterns correspond to turning a memory-less sequence into a sequence with memory. The memory effects are stronger the...

We analyze the data of the Italian and U.S. futures on the stock markets and we test the validity of the Continuous Time Random Walk assumption for the survival probability of the returns time series via a renewal aging experiment. We also study the survival probability of returns sign and apply...

We discuss a route to intermittency based on the concept of reflexivity, namely on the interaction between observer and stochastic reality. A simple model mirroring the essential aspects of this interaction is shown to generate perennial out of equilibrium condition, intermittency and 1/f-noise....

With the help of the diffusion entropy technique we show the non-Poisson statistics of the distances between consecutive Omori's swarms of earthquakes. We give an analytical proof of the numerical results of an earlier paper (Phys. Rev. Lett. 90 (2003) 188501).

A series of phenomenological macro-micro correlations is developed for single and multi-particle correlation functions descriptive of molecular rototranslation. The relation between hydrodynamic and molecular theories of molecular motion may then be investigated in the Markov limit. It is...

Symbolic sequences with long-range correlations are expected to result in a slow regression to a steady state of entropy increase. However, we prove that also in this case a fast transition to a constant rate of entropy increase can be obtained, provided that the extensive entropy of Tsallis...

The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional...