Related papers: Power-law versus exponential distributions of anim…
In a recent study of certain merging-splitting models of animal-group size (Degond et al., J. Nonl. Sci. 27 (2017) 379), it was shown that an initial size distribution with infinite first moment leads to convergence to zero in weak sense,…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
Power law size distribution is found to associate with fractal, self-organized behaviors and patterns of complex systems. Such distribution also emerges from natural lakes, with potentially important links to the dynamics of lake systems.…
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…
We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions…
From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior…
A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…
Current-day genomes bear the mark of the evolutionary processes. One of the strongest indications is the sequence homology among families of proteins that perform similar biological functions in different species. The number of proteins in…
We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no…
A simple model of biological extinction with variable system size is presented that exhibits a power-law distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman (Proc. R. Soc. Lond.…
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with…
Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has…
The distribution of species body size within taxonomic groups exhibits a heavy right-tail extending over many orders of magnitude, where most species are significantly larger than the smallest species. We provide a simple model of…
Universal scaling in the power-law size distribution of pelagic fish schools is established. The power-law exponent of size distributions is extracted through the data collapse. The distribution depends on the school size only through the…