title: Stochastic bifurcations in the nonlinear parallel Ising model.
abstract: We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.
authors.affiliation: Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, and INFN-Istituto Nazionale di Fisica Nucleare-Sezione di Firenze Via Giovanni Sansone 1, I-50019 Sesto Fiorentino, 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