A dynamical systems model of unorganized segregation

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.