Dynamical systems of self-organized segregation

We re-consider Schelling’s (1971) bounded neighbourhood model as put into the form of a dynamical system by Haw and Hogan (2018). In the case of a single neighbourhood we explain the occurring bifurcation set, thereby correcting a minor scaling error. In the case of two neighbourhoods we correct a major error and derive a dynamical system that does satisfy the modeling assumptions made by Haw and Hogan (2020), staying as close as possible to their construction. We find that stable integration then is only possible if the populations in the two neighbourhoods have the option to be in neither neighbourhood. In the absence of direct movement between the neighbourhoods the problem is furthermore equivalent to independent single neighbourhood problems.