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Modeling and numerical simulations of the influenced Sznajd model
Farshad Salimi Naneh Karan1, Aravinda Ramakrishnan Srinivasan1, Subhadeep Chakraborty1
1Department of Mechanical, Aerospace, and Biomedical Engineering at University of Tennessee, Knoxville, Tennessee 37996, USA.
Independent nonconformists, or influencers, significantly alter population behavior dynamics in the Sznajd model. Their distribution determines system convergence to unique steady-state probability distribution functions (PDFs).
Area of Science:
- Complex Systems
- Statistical Physics
- Agent-Based Modeling
Background:
- The Sznajd model describes social influence and opinion formation in interacting agent populations.
- Understanding the impact of dissenting opinions or influential individuals is crucial for social dynamics.
- Previous models often focus on consensus without fully exploring the role of nonconformists.
Purpose of the Study:
- To investigate how independent nonconformists (influencers) affect the behavioral dynamics of agents in the Sznajd model.
- To analyze the system's convergence properties and steady-state behaviors based on influencer distribution.
- To examine the scaling properties and entropy of the system under varying levels of influence.
Main Methods:
- Modeling the agent population on a complete graph.
- Utilizing the master equation to describe the system's dynamics.
- Numerically solving the derived master equation and validating with simulations.
Main Results:
- Identified specific regions of initial magnetization from which the system converges.
- Demonstrated that the system converges to one of two unique steady-state probability distribution functions (PDFs).
- The specific steady-state PDF is dependent on the distribution of influencers within the population.
Conclusions:
- The presence and distribution of influencers critically shape the collective behavior of agent populations.
- The Sznajd model, when incorporating influencers, exhibits predictable convergence patterns.
- Analysis of scaling properties and entropy provides insights into system stability and information flow.
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