Phase transition in cellular automata model of opinion dynamics
Janusz Holyst
Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, POLAND
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We study a model of opinion formation based on the theory of social impact
and the concept of cellular automata. The case is considered when a strong
leader is present in the group. There are two basic stationary states of
the system: cluster of the leader's adherents and unification of
opinions. In the deterministic limit the variation of parameters like the
leader's strength or external impact can change the size of the cluster
or, when they reach some critical values, make the system jump to another
phase. For a certain range of parameters multistability and hysteresis
phenomena are observed. In the presence of noise (social temperature) the
rapid changes can be regarded as the first-order phase transitions.
Appearance of a strong leader can be explained by the active agent model
of social strength evolution. Analytical results obtained within a mean
field approximation are well reproduced in computer simulations.
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