Related papers: Modelling bursty time series
We introduce a toy model displaying the avalanche dynamics of failure in scale-free networks. In the model, the network growth is based on the Barab\'asi and Albert model and each node is assigned a capacity or tolerance, which is constant…
Particles floating on the surface of a turbulent incompressible fluid accumulate along string-like structures, while leaving large regions of the flow domain empty. This is reflected experimentally by a very peaked probability distribution…
The long-time dynamics of the 1D contact process suddenly brought out of an uncorrelated initial state is studied through a light-cone transfer-matrix renormalisation group approach. At criticality, the system undergoes ageing which is…
An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent:…
Empirical analysis show that, after the update of a browser, the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older version, or being not yet patched, or…
Intermittent transitions, associated with critical dynamics and characterized by power-law distributions, are commonly observed during sleep. These critical behaviors are evident at the microscopic level through neuronal avalanches and at…
Temporal analyses of the prompt gamma-ray and X-ray light curves of gamma-ray bursts reveal a tendency for the burst pulse time scales to increase with decreasing energy. For an ensemble of BATSE bursts, Fenimore et al. (1995) show that the…
We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $\alpha \in (0,1]$ and the service completions are triggered by an independent fractional Poisson…
Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of…
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in…
Taylor's power law (or fluctuation scaling) states that on comparable populations, the variance of each sample is approximately proportional to a power of the mean of the population. It has been shown to hold by empirical observations in a…
A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time thermal bath dynamics, similar to random Ising systems. The interactions between agents change…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
Gamma-ray burst time histories often consist of many peaks. These peaks tend to be narrower at higher energy. If gamma-ray bursts are cosmological, the energy dependence of gamma-ray burst time scales must be understood in order to correct…
Decay law of a complicated unstable state formed in a high energy collision is described by the Fourier transform of the two-point correlation function of the scattering matrix. Although each constituent resonance state decays exponentially…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively…
Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve…
We study the statistical properties of time distribution of seimicity in California by means of a new method of analysis, the Diffusion Entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…