Stylianos Scarlatos

We investigate the one-dimensional dynamics of alternatives of the Axelrod model (ξ(t)), where t is the time, 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 (ξ(t)) is emulated by a corresponding attractive model (η(t)) with the same parameters (conditional on bounded confidence). (η(t)) is more mathematically tractable than (ξ(t)), 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, (η(t)) fixates (each site has a final type independent of the possibly infinite size of the lattice), whereas (ξ(t)) fluctuates (each site changes type at arbitrarily larger times t as the size of the lattice increases).

The discrete Deffuant model and its alternatives is a family of stochastic spatial models for the dynamics of binary opinions on f issues. Another parameter is also incorporated that prevents interaction between two agents whenever their opinion profiles are at a Hamming distance greater than the confidence threshold θ. By numerical simulations, it was conjectured in (Adamopoulos and Scarlatos, Complexity 2012, 17, 43) that one‐dimensional models exhibit a phase transition at a critical value θ critical approximately equal to f/2. We report on recent mathematical results on this problem that originates from the community of complex systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 437–439, 2016