A dynamical systems model of unorganized segregation in two neighborhoods

We present a complete analysis of the Schelling dynamical system of two connected neighborhoods, 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 neighborhood, 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 neighborhood may not remain so when a connecting neighborhood is created.