Related papers: Widening Disparity and its Suppression in a Stocha…
Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
This paper consider a highly general dissemination model that keeps track of the stochastic evolution of the distribution of wealth over a set of agents. There are two types of events: (i) units of wealth externally arrive, and (ii) units…
We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We…
We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
A dynamical model for the distribution of resources between competing agents is studied. While global competition leads to the accumulation of all the resources by a single agent, local competition allows for a wider resource distribution.…
Natural selection and random drift are competing phenomena for explaining the evolution of populations. Combining a highly fit mutant with a population structure that improves the odds that the mutant spreads through the whole population…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
We present a dynamical model of web site growth in order to explore the effects of competition among web sites and to determine how they affect the nature of markets. We show that under general conditions, as the competition between sites…
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 behavior of linear discriminant functions for binary classification in the infinite-imbalance limit, where the sample size of one class grows without bound while the sample size of the other remains fixed. The coefficients of…
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…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
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…
Lifetime distributions of social entities, such as enterprises, products, and media contents, are one of the fundamental statistics characterizing the social dynamics. To investigate the lifetime distribution of mutually interacting…
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…