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Simplicity of rumor self-organization revealed by unstable eigenvectors and amplitudes

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  • T. D. Frank

    (University of Connecticut
    University of Connecticut)

Abstract

It is shown that unstable eigenvectors determine the manner in which the subpopulations involved in rumor spreading organize themselves when initially spreading out rumors. The corresponding amplitudes may determine temporal aspects of rumor spreading even beyond the linear domain of the eigenvector analysis. In doing so, eigenvectors and amplitudes taken together can reveal the relatively simply organization of rumor spreading. For the benchmark Daley-Kendall model it is demonstrated that the eigenvector determines the rumor spreading organization in all three fundamental cases of rumor spreading suggested by Pequeira. Moreover, the approach is applied to the Earth-is-flat rumor that circulated during spring 2017. The analysis suggests that subpopulations organization was characterized by a 21:25 ratio such that per 25 initially ignorant community members 21 spreaders occurred, a ratio that is close to the optimal 1:1 ratio that would indicate that every ignorant member turned into a spreader.

Suggested Citation

  • T. D. Frank, 2025. "Simplicity of rumor self-organization revealed by unstable eigenvectors and amplitudes," Computational and Mathematical Organization Theory, Springer, vol. 31(1), pages 1-26, March.
    • Handle: RePEc:spr:comaot:v:31:y:2025:i:1:d:10.1007_s10588-024-09393-y
    DOI: 10.1007/s10588-024-09393-y
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    References listed on IDEAS

    as
    1. T. D. Frank, 2020. "Simplicity From Complexity: On The Simple Amplitude Dynamics Underlying Covid-19 Outbreaks In China," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 23(08), pages 1-24, December.
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    6. T. D. Frank, 2021. "COVID-19 outbreaks follow narrow paths: A computational phase portrait approach based on nonlinear physics and synergetics," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(08), pages 1-16, August.
    7. Bodaghi, Amirhosein & Goliaei, Sama & Salehi, Mostafa, 2019. "The number of followings as an influential factor in rumor spreading," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 167-184.
    8. T. D. Frank, 2024. "Amplitude Equations And Order Parameters Of Human Sars-Cov-2 Infections And Immune Reactions: A Model-Based Approach," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 27(01n02), pages 1-42, March.
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