Blume-Emery-Griffiths Dynamics In Social Networks

Recently, there has been a growing interest in the study of complex systems. In particular, one of the hot research topics is opinion formation which treated as a collective phenomenon about society. In general, there are some analytical solution and numerical results base on simple network structure and dynamics, which are different with realistic social systems.In this thesis, we introduce the Blume-Emery-Griffiths model to describe the dynamics of opinion formation firstly, and the more real social network is studied. The results show the probability distribution function associated with the time series of opinion is a like-Gaussian distribution. Comparing with the parameter of entropy and autocorrelation function for the time series of Dow-Jones Index's daily logarithmic returns, it was found there exist similar behaviors between them. We also study the effect of external field on networks. It was observed phase transition occurs by interior thermo-noise, which is very similar with Ising model, and by external field. Specially, it is interesting that the split of opinion distribution was observed under some suitable situations and the frequency and initial phase have a quasi periodic influence for systems.There are four parts in this thesis.In the first chapter, we present a brief introduction on complex networks, including the dimensions and the main characters for some famous models.In the second chapter, we introduce the opinion formation, mainly focused on analytical solution and the numerical results.In the third chapter, we present our works, including the dynamical equation, the method of constructing social networks, and our simulation results. A summary was presented in the last chapter.