title: Bifurcations in models of a society of reasonable contrarians and conformists.
abstract: We study models of a society composed of a mixture of conformist and reasonable contrarian agents that at any instant hold one of two opinions. Conformists tend to agree with the average opinion of their neighbors and reasonable contrarians tend to disagree, but revert to a conformist behavior in the presence of an overwhelming majority, in line with psychological experiments. The model is studied in the mean-field approximation and on small-world and scale-free networks. In the mean-field approximation, a large fraction of conformists triggers a polarization of the opinions, a pitchfork bifurcation, while a majority of reasonable contrarians leads to coherent oscillations, with an alternation of period-doubling and pitchfork bifurcations up to chaos. Similar scenarios are obtained by changing the fraction of long-range rewiring and the parameter of scale-free networks related to the average connectivity.
authors.affiliation: Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, 50017 Sesto Fiorentino, Firenze, Italy and INFN, Sezione di Firenze, Firenze, Italy.
authors.forename: Franco
authors.initials: F
authors.lastname: Bagnoli
authors.affiliation: Instituto de Energías Renovables, Universidad Nacional Autónoma de México, Apartado Postal 34, 62580 Temixco, Morelos, Mexico.
authors.forename: Raúl
authors.initials: R
authors.lastname: Rechtman