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Published on: October 19, 2021
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Consensus and clustering in opinion formation on networks
Julia Bujalski1, Grace Dwyer2, Todd Kapitula3
1Department of Mathematics, Emmanuel College, Boston, MA 02115, USA.
Summary
This study extends opinion dynamics models to multiple communities, revealing conditions for consensus or pluralism. It shows how network structure, like hubs with zealots, can lead to widespread opinion adoption.
Area of Science:
- Socio-physics
- Mathematical modeling
- Network science
Background:
- Traditional opinion dynamics models assume isolated communities and uniform space.
- Ordinary differential equation (ODE) models are commonly used.
Purpose of the Study:
- To extend ODE models of opinion dynamics to incorporate multiple interacting communities.
- To analyze conditions leading to consensus and pluralism in networked systems.
Main Methods:
- Developed extended ODE models representing opinion dynamics on directed graphs.
- Utilized elementary bifurcation analysis for network structures.
- Performed numerical simulations for specific graph configurations (cycle graphs, hubs).
Main Results:
- Identified conditions for achieving system-wide consensus or maintaining pluralism.
- Demonstrated how network topology, such as cycle graphs, influences opinion clustering.
- Showed that a critical proportion of 'zealots' in a central hub can drive the entire network's opinion.
Conclusions:
- Network structure significantly impacts opinion dynamics and emergent behaviors.
- The extended ODE framework provides valuable insights into complex social opinion formation.
- Targeting influential nodes (hubs) with specific opinions can be an effective strategy for opinion dissemination.
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