Dynamics of group formation

TL;DR

This paper studies a dynamical system modeling group formation, revealing how group densities evolve and stabilize based on initial conditions, with implications for understanding collective behaviors.

Contribution

It introduces a novel dynamical model combining gradient competition and accumulation within groups, analyzing steady-state behaviors of group size distributions.

Findings

Group densities depend on initial single-element group densities.

Steady-state distributions exhibit interesting patterns based on initial conditions.

The model provides insights into the dynamics of group formation processes.

Abstract

We consider a specific dynamical system of groups formation. It is based simultaneously on a gradient competition between groups and a strong accumulation inside groups. Such a dynamical system demonstrates interesting behavior of densities of emerging groups of $1$, $2$, $3$, ... elements in a steady-state depending on the densities of one-elements groups in a randomly chosen initial state.