A dynamical systems model of unorganized segregation

ABSTRACT

We consider Schelling’s bounded neighborhood model (BNM) of unorganized segregation, from the perspective of modern dynamical systems theory. We carry out a complete quantitative analysis of the system for linear tolerance schedules. We derive a fully predictive model and associate each term with a social meaning. We recover and generalize Schelling’s qualitative results.

For the case of unlimited population movement, we derive exact formulae for regions in parameter space where stable integrated population mixes can occur, and show how neighborhood tipping can be explained in terms of basins of attraction.

When population movement is limited, we derive exact criteria for the occurrence of new population mixes.

For nonlinear tolerance schedules, we illustrate our approach with numerical simulations.

KEYWORDS:

• Unorganized Segregation
• Schelling
• Bounded Neighbourhood Model
• Dynamical System

Acknowlegments

We would like to thank Professor Simon Burgess of the University of Bristol for first suggesting the development of Schelling’s bounded neighborhood model.

DJH thanks the EPSRC for funding from the Bristol Centre for Complexity Sciences, reference EP/I013717/1.

Additional information

Funding

This work was supported by the Engineering and Physical Sciences Research Council [EP/I013717/1]. This study did not involve any underlying data.