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Anti-diffusion in continuous opinion dynamics

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  • Alexanian, Moorad
  • McNamara, Dylan

Abstract

Considerable effort using techniques developed in statistical physics has been aimed at numerical simulations of agent-based opinion models and analysis of their results. Such work has elucidated how various rules for interacting agents can give rise to steady state behaviors in the agent populations that vary between consensus and fragmentation. At the macroscopic population level, analysis has been limited due to the lack of an analytically tractable governing macro-equation for the continuous population state. We use the integro-differential equation that governs opinion dynamics for the continuous probability distribution function of agent opinions to develop a novel nonlinear partial differential equation for the evolution of opinion distributions. The highly nonlinear equation allows for the generation of a system of approximations. We consider three initial population distributions and determine their small-time behavior. Our analysis reveals how the generation of clusters results from the interplay of diffusion and anti-diffusion and how initial instabilities arise in different regions of the population distribution.

Suggested Citation

  • Alexanian, Moorad & McNamara, Dylan, 2018. "Anti-diffusion in continuous opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1256-1262.
    • Handle: RePEc:eee:phsmap:v:503:y:2018:i:c:p:1256-1262
    DOI: 10.1016/j.physa.2018.08.154
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    References listed on IDEAS

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    1. Boon, Jean Pierre & Lutsko, James F., 2006. "Generalized diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 55-62.
    2. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    3. Guillaume Deffuant & David Neau & Frederic Amblard & Gérard Weisbuch, 2000. "Mixing beliefs among interacting agents," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 3(01n04), pages 87-98.
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