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Finite-size effects on the convergence time in continuous-opinion dynamics.

Hang-Hyun Jo1, Naoki Masuda2,3

  • 1Department of Physics, The Catholic University of Korea, Bucheon 14662, Republic of Korea.

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|August 20, 2021
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Summary
This summary is machine-generated.

Finite-size effects impact opinion convergence time. On lattices, convergence slows with size, but on random graphs, it remains stable, revealing network structure

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Area of Science:

  • Complex Systems
  • Network Science
  • Sociophysics

Background:

  • Continuous-opinion dynamics models explore how collective opinions emerge.
  • Understanding finite-size effects is crucial for realistic social simulations.

Purpose of the Study:

  • To investigate how system size influences convergence time in continuous-opinion dynamics.
  • To compare these effects across different network topologies.

Main Methods:

  • Numerical simulations of opinion dynamics on various network types (lattices, random graphs, scale-free networks, complete graphs).
  • Mathematical analysis using a mean-field approach for complete graphs.

Main Results:

  • Convergence time increases with system size on lattice networks following a specific functional form.
  • Convergence time is largely independent of system size on random, scale-free, and complete graphs, provided partial opinion copying.
  • Mean-field analysis explains the behavior observed in complete graphs.

Conclusions:

  • Network topology significantly moderates finite-size effects on opinion convergence.
  • Partial opinion copying leads to size-independent convergence on many complex networks, unlike structured lattices.