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    Analysis of a nonlinear opinion dynamics model with biased assimilation

    Access Status
    In process
    Authors
    Xia, W.
    Ye, Mengbin
    Liu, J.
    Cao, M.
    Sun, X.M.
    Date
    2020
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Xia, W. and Ye, M. and Liu, J. and Cao, M. and Sun, X.M. 2020. Analysis of a nonlinear opinion dynamics model with biased assimilation. Automatica. 120.
    Source Title
    Automatica
    DOI
    10.1016/j.automatica.2020.109113
    ISSN
    0005-1098
    Faculty
    Faculty of Science and Engineering
    School
    School of Elec Eng, Comp and Math Sci (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/82651
    Collection
    • Curtin Research Publications
    Abstract

    © 2020 Elsevier Ltd This paper analyzes a nonlinear opinion dynamics model which generalizes the DeGroot model by introducing a bias parameter for each individual. The original DeGroot model is recovered when the bias parameter is equal to zero. The magnitude of this parameter reflects an individual's degree of bias when assimilating new opinions, and depending on the magnitude, an individual is said to have weak, intermediate, and strong bias. The opinions of the individuals lie between 0 and 1. It is shown that for strongly connected networks, the equilibria with all elements equal identically to the extreme value 0 or 1 is locally exponentially stable, while the equilibrium with all elements equal to the neutral consensus value of 1/2 is unstable. Regions of attraction for the extreme consensus equilibria are given. For the equilibrium consisting of both extreme values 0 and 1, which corresponds to opinion polarization according to the model, it is shown that the equilibrium is unstable for all strongly connected networks if individuals all have weak bias, becomes locally exponentially stable for complete and two-island networks if individuals all have strong bias, and its stability heavily depends on the network topology when individuals have intermediate bias. Analysis on star graphs and simulations show that additional equilibria may exist where individuals form clusters.

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