Analysis of a nonlinear opinion dynamics model with biased assimilation
© 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...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
2020
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| Online Access: | http://purl.org/au-research/grants/arc/DP160104500 http://hdl.handle.net/20.500.11937/82651 |
| _version_ | 1848764529789370368 |
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| author | Xia, W. Ye, Mengbin Liu, J. Cao, M. Sun, X.M. |
| author_facet | Xia, W. Ye, Mengbin Liu, J. Cao, M. Sun, X.M. |
| author_sort | Xia, W. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 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. |
| first_indexed | 2025-11-14T11:20:49Z |
| format | Journal Article |
| id | curtin-20.500.11937-82651 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:20:49Z |
| publishDate | 2020 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-826512022-10-27T06:11:39Z Analysis of a nonlinear opinion dynamics model with biased assimilation Xia, W. Ye, Mengbin Liu, J. Cao, M. Sun, X.M. © 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. 2020 Journal Article http://hdl.handle.net/20.500.11937/82651 10.1016/j.automatica.2020.109113 http://purl.org/au-research/grants/arc/DP160104500 http://purl.org/au-research/grants/arc/DP190100887 fulltext |
| spellingShingle | Xia, W. Ye, Mengbin Liu, J. Cao, M. Sun, X.M. Analysis of a nonlinear opinion dynamics model with biased assimilation |
| title | Analysis of a nonlinear opinion dynamics model with biased assimilation |
| title_full | Analysis of a nonlinear opinion dynamics model with biased assimilation |
| title_fullStr | Analysis of a nonlinear opinion dynamics model with biased assimilation |
| title_full_unstemmed | Analysis of a nonlinear opinion dynamics model with biased assimilation |
| title_short | Analysis of a nonlinear opinion dynamics model with biased assimilation |
| title_sort | analysis of a nonlinear opinion dynamics model with biased assimilation |
| url | http://purl.org/au-research/grants/arc/DP160104500 http://purl.org/au-research/grants/arc/DP160104500 http://hdl.handle.net/20.500.11937/82651 |