Mean field models for segregation dynamics

TL;DR

This paper develops and analyzes mean-field models describing how groups of individuals, influenced by perceived densities and space, tend to aggregate or segregate, revealing complex dynamics through theoretical and numerical analysis.

Contribution

It introduces two novel mean-field models capturing segregation dynamics based on local and non-local interactions, with analysis of their stability and solution properties.

Findings

Models exhibit aggregation and segregation behaviors.

Existence and stability of solutions are established.

Numerical simulations illustrate complex dynamics.

Abstract

In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well as the available space. All individuals have the tendency to stay within their own group and avoid the others. These interactions lead to the formation of aggregates in case of a single species, and to segregation in the case of multiple species. We derive two different mean-field models, which are based on these interactions and weigh local and non-local effects differently. We discuss existence and stability properties of solutions for both models and illustrate the rich dynamics with numerical simulations.