Abstract

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).