Related papers: Forcing anomalous scaling on demographic fluctuati…
A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare,…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.
This work investigates the influence of a generic anomalous diffusion model on mass convection in a fluid-saturated porous medium, focusing on superdiffusive regimes. A mathematical model is developed, and tability analyses - both linear…
We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just…
A one-dimensional Hamiltonian system with exponential interactions perturbed by a conservative noise is considered. It is proved that energy superdiffuses and upper and lower bounds describing this anomalous diffusion are obtained
A simulation model of a population having internal (genetic) structure is presented. The population is subject to selection pressure coming from the environment which is the same in the whole system but changes in time. Reproduction has a…
Scale-invariant spatial or temporal patterns and L\'evy flight motion have been observed in a large variety of biological systems. It has been argued that animals in general might perform L\'evy flight motion with power law distribution of…
Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
The abundance of a species' population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a…
Nonequilibrium systems with large-scale fluctuations of a suitable system parameter are often effectively described by a superposition of two statistics, a superstatistics. Here we illustrate this concept by analysing experimental data of…
The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by "viscoelastic" anomalous diffusion, in which the increments of the motion feature…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
We experimentally study anomalous diffusion of ultra-cold atoms in a one dimensional polarization optical lattice. The atomic spatial distribution is recorded at different times and its dynamics and shape are analyzed. We find that the…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
Fluctuation scaling (FS) and anomalous diffusion have been discussed in different contexts, even though both are often observed in complex systems. To clarify the relationship between these concepts, we investigated approximately three…
We argue that atmospheric cascades can be regarded as example of the self-organized criticality and studied by using Levy flights and nonextensive approach. It allows us to understand the scale-invariant energy fluctuations inside cascades…
In this paper we analyze a coupling between the very large jumps in physical and operational times as applied to anomalous diffusion. The approach is based on subordination of a skewed Levy-stable process by its inverse to get two types of…