Social impact model with strong leader and external field: mean field-like approach
Author: Krzysztof Kacperski
Janusz Holyst
A model of two-state opinion formation based on the theory of social impact and the
concept of cellular automata is studied.
The case is considered when two strong agents influence the group: a strong leader and an
external social impact acting uniformly on every individual.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 of the global opinion distribution can be regarded as the first order phase
transitions. When both agents are in a kind of balance, a second order transition and
critical behaviour can be observed. Another kind of noise induced transitions are the
inverses (flips) of the unified group opinion due to random flips of the leader's opinion.
Analytical results obtained within a mean field approximation are well reproduced in
computer simulations.
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