SCALING PHENOMENA IN THE SLOPE SYSTEM

Abstract

An agent-based model is applied for studying the group-forming behavior numerically. A fixed number of homogeneous agents are distributed on a two-dimensional square lattice system with L × L unit cells. The dynamics of the agents are described in terms of a potential and a friction factor, just like that of a weight on a slope. The potential is defined in an attempt to model the concept of the "biosocial attraction." Depending on the density of the population and the friction factor, four regimes of group-size distributions are identified. They are the fixed, the exponential, the power-law and the black-hole regimes. Especially, beyond the well-known exponential and power-law distributions, a black-hole regime is identified for the lowest values of the friction factor. In the black-hole regime, all the agents in the system are attracted to the only group remaining in the system. An example membership values for each of the four classes are suggested in terms of the two key parameters of the system, the population density and the friction factor. And a phase transition is observed between the exponential and the black-hole regimes. Also the results are discussed in relation to the city-size distributions in a country.