Kinetic Models of Discrete Opinion Dynamics on Directed Barabási–Albert Networks

F. Welington S. Lima,J. A. Plascak

doi:10.3390/e21100942

Abstract

Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class.

Highlights

There has been, recently, a great interest in the study of networks [1,2,3], which are different from the regular crystalline Bravais lattices, and are frequently called scale-free networks
It is clear from these figures that the system undergoes a second-order phase transition, since the cumulants tend to cross at the same value at the critical disorder parameter pc [11]
We have studied a discrete version of the non-equilibrium kinetic Biswas-Chatterjee-Sen (BCS)

Summary

Introduction

There has been, recently, a great interest in the study of networks [1,2,3], which are different from the regular crystalline Bravais lattices, and are frequently called scale-free networks. Spin systems defined on such complex networks have been considered in the purpose to determine the character of its phase transition, if present, and the corresponding universality class in the case of critical behavior (for a recent review see reference [4]). In the particular case of the directed Barabási–Albert networks (DBAN), it has been shown that the nearest-neighbor spin-1/2 Ising model has no phase transition [4,5,6]. On these same networks the non-equilibrium majority-vote model (MVM) [7] presents a well-defined order–disorder dynamical phase transition [8].

Biswas-Chatterjee-Sen Model

Simulations

Results and Discussion

Conclusions