Opinion Dynamics On The Complex Networks

Complex network is an significant method to study complex system, the goal ofcomplex network research is to understand how the structure of influence the physicsprocess on the networks. On the basis of complex network theory, the opinion dynamicson the complex network has been studied in this thesis.The dynamics of agreement or disagreement among individuals is complexbecause the individuals are. Statistical physicists working on opinion dynamics aim atdefining the opinion states of a population and the elementary processes that determinetransitions between such states. In the past decade, many models have been designed,we focus on the models that have received more attention in the physics literature,pointing out analogies as well as differences between them.This paper is main focusing on the subject:”The voter model”. Through modifyingthe rule, an extended majority vote model is presented. Comparing with the theoreticaland simulation results, we give the quantitative analysis in the complex networks. Thispaper’s main work can be listed as follow:1. Aiming at the influence of the super-node on the opinion formation in the actuallife, we study an extended majority vote model with a super-node on regular lattices. Inthe paper, applying the pair approximation approach, we compare our theoretical resultswith the simulation results with and without a super-node and make a quantitativeanalysis with a super-node. Aiming at the influence of the super-node and optimalcontrol strategies for an advertising competing model, we present an extended majorityvote model to study the optimal advertisement model in different communities. MonteCarlo simulation of the models shows that there is a certain linear relationship betweenthe total opinion density and super-node intensity. Based on such a linear relationship,we can get a optimal advertisement model.2. Jia Shao. propose a non-consensus opinion(NCO) model, in which coexistenceof minority and majority opinions occurs. the authors pointed out that NCO model in a2D regular lattice has a2-periodic oscillation. we have presented an exact solution ofthe NCO model on the line, all cases are analyzed on the one-dimensional line byprobability. We find that the2-periodic oscillation is very remarkable in the NCO modeland we make a quantitative analysis on oscillation in the regular networks and giveseveral necessary conditions, under which an oscillation can occur.