Abstract
We study the dynamics of three populations evolving in a two-dimensional discrete grid according to rules of attraction, rejection, or indifference following the framework of the seminal model by Sakoda and we apply it to migration phenomena. An interesting feature of the Sakoda model is the existence of a Potts-like energy which, as a common principle, decreases as time passes by. Here we consider the evolution of two populations until stabilization, then, we perturb this attractor by the inclusion of a third arrival: the immigrants. We show the conditions under which this irruption does not alter significantly the previous attractor (a sociological morphostatic behaviour) or it is dramatically changed (morphogenetic behaviour). We observe empirically that for a morphostatic behaviour the energy decreases while for morphogenesis this energy increases, revealing an escalation of social tension.
Highlights
We study the dynamics of three populations evolving in a two-dimensional discrete grid according to rules of attraction, rejection, or indifference following the framework of the seminal model by Sakoda and we apply it to migration phenomena
The same procedure can be repeated for other social structures, in this paper we present the morphostasis-morphogenesis transition in the cases of these two social structures: S1 and S5
We develop a generalization of Sakoda’s model for three populations to study the dynamics and social consequences of immigration phenomena on social structures
Summary
We study the dynamics of three populations evolving in a two-dimensional discrete grid according to rules of attraction, rejection, or indifference following the framework of the seminal model by Sakoda and we apply it to migration phenomena. The principles of the seminal model are simple: two groups with positive, neutral or negative attitudes to one another moving in an 8 × 8 chessboard (the space of interaction), trying to improve their position according to the value of a field that takes into account the social preferences of the two populations as well as the distance between individuals. The basic rule of the model consists of the following steps: first, to take a random individual; to evaluate its social expectation at all possible empty sites, the individual moves to the position giving the highest “potential” expectation. This procedure is repeated randomly among all possible individuals
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