Entry limitations and heterogeneous tolerances in a Schelling-like segregation model

Abstract In this paper we consider a Schelling-type segregation model with two groups of agents that differ in some aspects, such as religion, political affiliation or color of skin. The first group is identified as the local population, while the second group is identified as the newcomers, whose members want to settle down in the city or country, or more generally a system, already populated by members of the local population. The members of the local population have a limited tolerance towards newcomers. On the contrary, some newcomers, but not all of them, may stand the presence of any amount of members of the local population. The heterogeneous, and partially limited, levels of tolerance trigger an entry and exit dynamics into and from the system of the members of the two groups based on their satisfaction with the number of members of the other group into the system. This entry/exit dynamics is described by a continuous piecewise-differentiable map in two dimensions. The dynamics of the model is characterized by smooth bifurcations as well as by border collision bifurcations. A combination of analytical results and numerical analysis are the main tools used to describe the quite complicated local and global dynamics of the model. The investigation reveals that two factors are the main elements that preclude integration. The first one is a low level of tolerance of the members of the two populations. The second one is an excessive and unbalanced level of tolerance between the two populations. In this last case, to facilitate the integration between members of the two groups, we impose an entry-limitation policy represented by the imposition of a maximum number of newcomers allowed to enter the system. The investigation of the dynamics reveals that the entry-limitation policy is useful to promote integration as it limits the negative effects due to excessive and unbalanced levels of tolerance.

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