Abstract
This paper considers the models of tolerance originating from the well-known Schelling’s publication. It is demonstrated that tolerant threshold behavior (including Schelling’s model) can be reduced to Granovetter’s model with a definite threshold distribution function. We study a model describing competition within a group simultaneously with absolute sympathy for an opposite group (a sort of “converse tolerance”). These two types of behavior are examined in continuous time, taking into account the effects of forgetting and delay that cause damped and sustained oscillating processes.
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Schelling, T., Dynamic Models of Segregation, J. Math. Sociology, 1971, vol. 1, pp. 143–186.
Granovetter, M., Threshold Models of Collective Behavior, AJS, 1978, vol. 83, no. 6, pp. 1420–1443.
Breer, V.V., Conformity Behavior Models. I. From Philosophy to MathematicalModels, Probl. Upravlen., 2014, no. 1, pp. 2–13.
Breer, V.V., Conformity Behavior Models. II. Mathematical Models, Probl. Upravlen., 2014, no. 2, pp. 2–17.
Slovokhotov, Yu.L., Physics vs. Sociophysics, I–III, Probl. Upravlen., 2012, no. 1, pp. 2–20; no. 2, pp. 2–31; no. 3, pp. 2–34.
Hatna, E. and Benenson, I., The Schelling Model of Ethnic Residential Dynamics: Beyond the Integrated—Segregated Dichotomy of Patterns, J. Artific. Soc. Social Simulation, 2012, vol. 15, no. 1. URL: http://jasss.soc.surrey.ac.uk/15/1/6.html (accessed November 26, 2015).
Dokumaci, E. and Sandholm, W., Schelling Redux: An Evolutionary Dynamic Model of Residential Segregation, Univ. of Wiscontine, June, 2007, pp. 1–37. URL: http://www.ssc.wisc.edu/~whs/research/schelling.pdf (accessed November 26, 2015).
Li, Z. and Tang, X., A Study of Collective Action Threshold Model Based on Utility and Psychological Theories, Lecture Notes in Computer Science, 2012, vol. 7669, pp. 474–482.
Kimmel, M.S., Revolution, a Sociological Interpretation, Philadelphia: Temple Univ. Press, 1990.
Breer, V.V., Game-theoretic Models of Collective Conformity Behavior, Autom. Remote Control, 2012, vol. 73, no. 10, pp. 1680–1692.
Kuznetsov, O.P., Complex Networks and Activity Spreading, Autom. Remote Control, 2015, vol. 76, no. 12, pp. 2091–2109.
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Original Russian Text © V.V. Breer, 2016, published in Problemy Upravleniya, 2016, No. 1, pp. 11–20.
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Breer, V.V. Models of tolerant threshold behavior (from T. Schelling to M. Granovetter). Autom Remote Control 78, 1304–1318 (2017). https://doi.org/10.1134/S0005117917070128
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DOI: https://doi.org/10.1134/S0005117917070128