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Emulation and complementarity in one-dimensional alternatives of the axelrod model with binary features

Authors

  • A. Adamopoulos,

    Corresponding author
    1. Department of Medicine, Medical Physics Laboratory, Democritus University of Thrace, 681 00 Alexandroupolis, Greece
    • Department of Medicine, Medical Physics Laboratory, Democritus University of Thrace, 681 00 Alexandroupolis, Greece
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  • S. Scarlatos

    Corresponding author
    1. Department of Mathematics, Center for Research and Applications of Nonlinear Systems, University of Patras, Patra 265 00, Greece
    Current affiliation:
    1. Kabouridou 44, 552 36 Thessaloniki, Greece
    • Department of Mathematics, Center for Research and Applications of Nonlinear Systems, University of Patras, Patra 265 00, Greece
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Abstract

We investigate the one-dimensional dynamics of alternatives of the Axelrod model (ξt) with k binary features and confidence parameter ε = 0, 1,…, k. Simultaneously, the simple Axelrod model is also critically examined. Specifically, for small and large ε, simulations suggest that the convergent model (ξt) is emulated by a corresponding attractive model (ηt) with the same parameters (conditional on bounded confidence). (ηt) is more mathematically tractable than (ξt), and the very definitions of the two qualitative behaviors of cyclic particle systems (fluctuation and fixation) are applicable in special cases. Moreover, we observe a complementarity: for not too small k and equation image, (ηt) fixates (each site has a final type independent of the possibly infinite size of the lattice), whereas (ξt) fluctuates (each site changes type at arbitrarily larger times t as the size of the lattice increases). © 2011 Wiley Periodicals, Inc. Complexity, 2011

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