  We consider Schelling's bounded neighbourhood model (BNM) of unorganised
segregation of two populations from the perspective of modern dynamical systems
theory. We derive a Schelling dynamical system and carry out a complete
quantitative analysis of the system for the case of a linear tolerance schedule
in both populations. In doing so, we recover and generalise 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. We show how neighbourhood tipping can be adequately
explained in terms of basins of attraction. For the case of limiting population
movement, we derive exact criteria for the occurrence of new population mixes
and identify the stable cases. We show how to apply our methodology to
nonlinear tolerance schedules, illustrating our approach with numerical
simulations. We associate each term in our Schelling dynamical system with a
social meaning. In particular we show that the dynamics of one population in
the presence of another can be summarised as follows
  {rate of population change} = {intrinsic popularity of neighbourhood} -
{finite size of neighbourhood} - {presence of other population}
  By approaching the dynamics from this perspective, we have a complementary
approach to that of the tolerance schedule.
