The role of constraints in a segregation model: the asymmetric case

We extend the analysis on the effects of the entry constraints on the dynamics of an adaptive segregation model of Shelling's type when the two populations involved differ in numerosity, level of tolerance toward members of the other population, and speed of reaction. The model is described by a two-dimensional piecewise smooth dynamical system in discrete time, where the entry constraints represent possible exogenous controls imposed by an authority in order to regulate the maximum number of members of the two populations allowed to enter the system, usually the district in which they live in. In this paper, we investigate the nature of some particular border collision bifurcations and discuss the policy implications of the entry constraints in terms of segregation. The investigation reveals that asymmetries in the level of tolerance of the two populations involved may lead to phenomena of overreaction or overshooting in the adjustment process. In order to avoid the risk of segregation, suitable entry limitations must be imposed at least on the more tolerant population