# A dynamical systems model of unorganised segregation in two neighbourhoods

## TL;DR

This paper analyzes a dynamical model of segregation in two connected neighborhoods, revealing conditions under which integration is stable and how population and tolerance influence segregation dynamics.

## Contribution

It provides a complete analysis of the Schelling dynamical system for two neighborhoods, highlighting how population size and tolerance affect stable integration.

## Key findings

- Stable integration requires a small minority and high combined tolerance.
- Limiting one population does not guarantee stable integration in connected neighborhoods.
- Increasing the majority's tolerance is necessary for a growing minority to stay integrated.

## Abstract

We present a complete analysis of the Schelling dynamical system [Haw2018] of two connected neighbourhoods, with or without population reservoirs, for different types of linear and nonlinear tolerance schedules. We show that stable integration is only possible when the minority is small and combined tolerance is large. Unlike the case of the single neighbourhood, limiting one population does not necessarily produce stable integration and may destroy it. We conclude that a growing minority can only remain integrated if the majority increases its own tolerance. Our results show that an integrated single neighbourhood may not remain so when a connecting neighbourhood is created.