A family of models for Schelling binary choices

We introduce and study a family of discrete-time dynamical systems to model binary choices based on the framework proposed by Schelling in 1973. The model we propose uses a gradient-like adjustment mechanism by means of a family of smooth maps and allows understanding and analytically studying the phenomena qualitatively described by Schelling. In particular, we investigate existence of steady states and their relation to the equilibria of the static model studied by Schelling, and we analyze local stability, linking several examples and considerations provided by Schelling with bifurcation theory. We provide examples to confirm the theoretical results and to numerically investigate the possible destabilizations, as well as the emergence of coexisting attractors. We show the existence of chaos for a particular example.