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Message survival and decision dynamics in a class of reactive complex systems subject to external fields

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  • Rodriguez Lucatero, C.
  • Schaum, A.
  • Alarcon Ramos, L.
  • Bernal-Jaquez, R.

Abstract

In this study, the dynamics of decisions in complex networks subject to external fields are studied within a Markov process framework using nonlinear dynamical systems theory. A mathematical discrete-time model is derived using a set of basic assumptions regarding the convincement mechanisms associated with two competing opinions. The model is analyzed with respect to the multiplicity of critical points and the stability of extinction states. Sufficient conditions for extinction are derived in terms of the convincement probabilities and the maximum eigenvalues of the associated connectivity matrices. The influences of exogenous (e.g., mass media-based) effects on decision behavior are analyzed qualitatively. The current analysis predicts: (i) the presence of fixed-point multiplicity (with a maximum number of four different fixed points), multi-stability, and sensitivity with respect to the process parameters; and (ii) the bounded but significant impact of exogenous perturbations on the decision behavior. These predictions were verified using a set of numerical simulations based on a scale-free network topology.

Suggested Citation

  • Rodriguez Lucatero, C. & Schaum, A. & Alarcon Ramos, L. & Bernal-Jaquez, R., 2014. "Message survival and decision dynamics in a class of reactive complex systems subject to external fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 338-351.
    • Handle: RePEc:eee:phsmap:v:405:y:2014:i:c:p:338-351
    DOI: 10.1016/j.physa.2014.03.024
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    References listed on IDEAS

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    1. Serge Galam, 2008. "Sociophysics: A Review Of Galam Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 409-440.
    2. Galam, Serge, 1997. "Rational group decision making: A random field Ising model at T = 0," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 238(1), pages 66-80.
    3. Serge Galam, 2007. "From 2000 Bush–Gore to 2006 Italian elections: voting at fifty-fifty and the contrarian effect," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(4), pages 579-589, August.
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