RESUMEN
A discrete version of opinion dynamics systems, based on the Biswas-Chatterjee-Sen (BChS) model, has been studied on Barabási-Albert networks (BANs). In this model, depending on a pre-defined noise parameter, the mutual affinities can assign either positive or negative values. By employing extensive computer simulations with Monte Carlo algorithms, allied with finite-size scaling hypothesis, second-order phase transitions have been observed. The corresponding critical noise and the usual ratios of the critical exponents have been computed, in the thermodynamic limit, as a function of the average connectivity. The effective dimension of the system, defined through a hyper-scaling relation, is close to one, and it turns out to be connectivity-independent. The results also indicate that the discrete BChS model has a similar behavior on directed Barabási-Albert networks (DBANs), as well as on Erdös-Rènyi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs). However, unlike the model on ERRGs and DERRGs, which has the same critical behavior for the average connectivity going to infinity, the model on BANs is in a different universality class to its DBANs counterpart in the whole range of the studied connectivities.
RESUMEN
We present an analysis of the quasistationary (QS) state of the contact process (CP) on annealed scale-free networks using a mapping of the CP dynamics in a one-step process and analyzing numerically and analytically the corresponding master equation. The relevant QS quantities determined via the master equation exhibit an excellent agreement with direct QS stochastic simulations of the CP. The high accuracy of the resulting data allows a probe of the strong corrections to scaling present in both the critical and supercritical regions, corrections that mask the correct finite-size scaling obtained analytically by applying an exact heterogeneous mean-field approach. Our results represent a promising starting point for a deeper understanding of the contact process and absorbing phase transitions on real (quenched) complex networks.
RESUMEN
We present high-accuracy quasistationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the anomalous finite-size scaling which was recently shown to hold for the contact process on annealed networks. It turns out that the quenched topology does not qualitatively change the critical behavior, leading only (as expected) to a shift of the transition point. The anomalous finite-size scaling holds with exactly the same exponents of the annealed case, so we can conclude that heterogeneous mean-field theory works for the contact process on quenched networks, at odds with previous claims. Interestingly, topological correlations induced by the presence of the natural cutoff do not alter the picture.
